Vector Addition, Subtraction, and Resolution

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JEE Main 2019, 10 Jan Shift-II

Two forces $P$ and $Q$ of magnitude $2 F$ and $3 F$ , respectively, are at an angle $θ$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $θ$ is

6 0^{\circ}

(B)

12 0^{\circ}

(C)

3 0^{\circ}

(D)

9 0^{\circ}

JEE Main 2021, 16 March Shift-I

LEVELJEE Main

Consider a frame that is made up of two thin massless rods $A B$ and $A C$ as shown in the figure. A vertical force $P$ of magnitude $100 N$ is applied at point $A$ of the frame. Suppose the force is $P$ resolved parallel to the arms $A B$ and $A C$ of the frame. The magnitude of the resolved component along the arm $A C$ is $x N$ . The value of $x$ , to the nearest integer, is ......... . [Given, $sin (3 5^{\circ}) = 0.573$ , $cos (3 5^{\circ}) = 0.819$ , $sin (11 0^{\circ}) = 0.939$ , $cos (11 0^{\circ}) = - 0.342$ ]

LEVELJEE Main

Two forces are such that the sum of their magnitudes is $18 N$ and their resultant which has magnitude $12 N$ , is perpendicular to the smaller force. Then, the magnitudes of the forces are

(A)

12 N, 6 N

(B)

13 N, 5 N

(C)

10 N, 8 N

(D)

16 N, 2 N

JEE Main 2021, 20 July Shift-II

LEVELJEE Main

Two vectors $P$ and $Q$ have equal magnitudes. If the magnitude of $P + Q$ is $n$ times the magnitude of $P - Q$ , then angle between $P$ and $Q$ is

(A)

sin^{- 1} (\frac{n - 1}{n + 1})

(B)

cos^{- 1} (\frac{n - 1}{n + 1})

(C)

sin^{- 1} (\frac{n ^{2} - 1}{n ^{2} + 1})

(D)

cos^{- 1} (\frac{n ^{2} - 1}{n ^{2} + 1})

JEE Main 2019, 10 Jan Shift-II

LEVELJEE Main

Two vectors $A$ and $B$ have equal magnitudes. The magnitude of $(A + B)$ is ' $n$ ' times the magnitude of $(A - B)$ . The angle between $A$ and $B$ is

(A)

sin^{- 1} (\frac{n ^{2} - 1}{n ^{2} + 1})

(B)

sin^{- 1} (\frac{n - 1}{n + 1})

(C)

cos^{- 1} (\frac{n ^{2} - 1}{n ^{2} + 1})

(D)

cos^{- 1} (\frac{n - 1}{n + 1})

JEE Main 2020 (7 Jan Shift-II)

LEVELJEE Main

The sum of two forces $P$ and $Q$ is $R$ such that $∣ R ∣ = ∣ P ∣$ . The angle $θ$ (in degrees) that the resultant of $2 P$ and $Q$ will make with $Q$ is, .........

JEE Main 2021, 25 July Shift-I

LEVELJEE Main

Match List I with List II.

List-I

(P)

C - A - B = 0

(Q)

A - C - B = 0

(R)

B - A - C = 0

(S)

A + B = - C

List-II

JEE Main 2021, 27 Aug Shift-I

LEVELJEE Main

The resultant of these forces OP, OQ, OR, OS and OT is approximately ...... N. [Take, $3 = 1.7$ , $2 = 1.4$ and given $\hat{i}$ and $\hat{j}$ unit vectors along X, Y axis]

(A)

9.25 \hat{i} + 5 \hat{j}

(B)

3 \hat{i} + 15 \hat{j}

(C)

2.5 \hat{i} - 14.5 \hat{j}

(D)

- 1.5 \hat{i} - 15.5 \hat{j}

JEE Main 2021, 27 July Shift-I

LEVELJEE Main

Assertion (A) If $A, B, C, D$ are four points on a semi-circular arc with centre at $O$ such that $∣ A B ∣ = ∣ B C ∣ = ∣ C D ∣$ , then $A B + A C + A D = 4 A O + O B + O C$ Reason (R) Polygon law of vector addition yields $A B + B C + C D + A D = 2 A O$ In the light of the above statements, choose the most appropriate answer from the options given below.

(A)

Both A and R are correct and R is the correct explanation of A.

(B)

Both A and R are correct but R is not the correct explanation of A.

(C)

A is correct but R is not correct.

(D)

A is not correct but R is correct.

JEE Main 2019, 10 Jan Shift-I

LEVELJEE Main

In the cube of side ' $a$ ' shown in the figure, the vector from the central point of the face $A B O D$ to the central point of the face $B E F O$ will be

(A)

\frac{1}{2} a (\hat{i} - \hat{k})

(B)

\frac{1}{2} a (\hat{j} - \hat{i})

(C)

\frac{1}{2} a (\hat{j} - \hat{k})

(D)

\frac{1}{2} a (\hat{k} - \hat{i})

JEE Main 2021, 25 July Shift-II

LEVELJEE Main

Two vectors $x$ and $y$ have equal magnitude. The magnitude of $(x - y)$ is $n$ times the magnitude of $(x + y)$ . The angle between $x$ and $y$ is

(A)

cos^{- 1} (\frac{- n ^{2} - 1}{n ^{2} - 1})

(B)

cos^{- 1} (\frac{1 - n ^{2}}{1 + n ^{2}})

(C)

cos^{- 1} (\frac{n ^{2} + 1}{- n ^{2} - 1})

(D)

cos^{- 1} (\frac{n ^{2} + 1}{n ^{2} - 1})

JEE Main 2021, 26 Aug Shift-I

LEVELJEE Main

The magnitude of vectors $O A$ , $O B$ , and $O C$ in the given figure are equal. The direction of $O A + O B - O C$ with X-axis will be

(A)

tan^{- 1} (\frac{1 - 3 - 2}{1 + 3 + 2})

(B)

tan^{- 1} (\frac{3 - 1 + 2}{1 + 3 - 2})

(C)

tan^{- 1} (\frac{3 - 1 + 2}{1 - 3 + 2})

(D)

tan^{- 1} (\frac{1 + 3 - 2}{1 - 3 - 2})

JEE Main 2021, 26 Aug Shift-II

LEVELJEE Advanced

The angle between vector $A$ and $(A - B)$ is

(A)

tan^{- 1} (\frac{- B /2}{A - B 3 /2})

(B)

tan^{- 1} (\frac{A}{0.7 B})

(C)

tan^{- 1} (\frac{3 B}{2 A - B})

(D)

tan^{- 1} (\frac{B c o s θ}{A - B s i n θ})

JEE Main 2021, 31 Aug Shift-II

LEVELJEE Main

Statement I Two forces $(P + Q)$ and $(P - Q)$ where $P ⊥ Q$ , when act at an angle $θ_{1}$ to each other, the magnitude of their resultant is $3 (P^{2} + Q^{2})$ , when they act at an angle $θ_{2}$ , the magnitude of their resultant becomes $2 (P^{2} + Q^{2})$ . This is possible only when $θ_{1} < θ_{2}$ . Statement II In the situation given above. $θ_{1} = 6 0^{\circ}$ and $θ_{2} = 9 0^{\circ}$ . In the light of the above statements, choose the most appropriate answer from the options given below.

(A)

Statement I is false but statement II is true.

(B)

Both statement I and statement II are true.

(C)

Statement I is true but statement II is false.

(D)

Both statement I and statement II are false.

JEE Advanced 2017

LEVELJEE Main

Three vectors $P$ , $Q$ and $R$ are shown in the figure. Let $S$ be any point on the vector $R$ . The distance between the points $P$ and $S$ is $b ∣ R ∣$ . The general relation among vectors $P$ , $Q$ and $S$ is

(A)

S = (1 - b^{2}) P + b Q

(B)

S = (b - 1) P + b Q

(C)

S = (1 - b) P + b Q

(D)

S = (1 - b) P + b^{2} Q

JEE Advanced 2018

LEVELJEE Advanced

Two vectors $A$ and $B$ are defined as $A = a \hat{i}$ and $B = a (cos ω t \hat{i} + sin ω t \hat{j})$ , where $a$ is a constant and $ω = π /6 rad s^{- 1}$ . If $∣ A + B ∣ = 3 ∣ A - B ∣$ at time $t = τ$ for the first time, the value of $τ$ , in seconds, is .............

JEE Advanced 1982

LEVELJEE Main

A particle is moving Eastwards with a velocity of $5$ m/s. In $10$ s, the velocity changes to $5$ m/s Northwards. The average acceleration in this time is

(A)

zero

(B)

\frac{1}{2}

m/s

^{2}

towards North-Eeast

(C)

\frac{1}{2}

m/s

^{2}

towards North-West

(D)

\frac{1}{2}

m/s

^{2}

towards North

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two vectors P and Q have equal magnitudes. If the magnitude of P+Q is n times the magnitude of P−Q, then angle between P and Q is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two vectors A and B have equal magnitudes. The magnitude of (A+B) is 'n' times the magnitude of (A−B). The angle between A and B is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The sum of two forces P and Q is R such that ∣R∣=∣P∣. The angle θ (in degrees) that the resultant of 2P and Q will make with Q is, .........

Match List I with List II.

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The resultant of these forces OP, OQ, OR, OS and OT is approximately ...... N. [Take, 3​=1.7, 2​=1.4 and given i^ and j^​ unit vectors along X, Y axis]

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two vectors x and y have equal magnitude. The magnitude of (x−y) is n times the magnitude of (x+y). The angle between x and y is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The magnitude of vectors OA, OB, and OC in the given figure are equal. The direction of OA+OB−OC with X-axis will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The angle between vector A and (A−B) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A particle is moving Eastwards with a velocity of 5 m/s. In 10 s, the velocity changes to 5 m/s Northwards. The average acceleration in this time is

Two vectors $P$ and $Q$ have equal magnitudes. If the magnitude of $P + Q$ is $n$ times the magnitude of $P - Q$ , then angle between $P$ and $Q$ is

Two vectors $A$ and $B$ have equal magnitudes. The magnitude of $(A + B)$ is ' $n$ ' times the magnitude of $(A - B)$ . The angle between $A$ and $B$ is

The sum of two forces $P$ and $Q$ is $R$ such that $∣ R ∣ = ∣ P ∣$ . The angle $θ$ (in degrees) that the resultant of $2 P$ and $Q$ will make with $Q$ is, .........

The resultant of these forces OP, OQ, OR, OS and OT is approximately ...... N. [Take, $3 = 1.7$ , $2 = 1.4$ and given $\hat{i}$ and $\hat{j}$ unit vectors along X, Y axis]

In the cube of side ' $a$ ' shown in the figure, the vector from the central point of the face $A B O D$ to the central point of the face $B E F O$ will be

Two vectors $x$ and $y$ have equal magnitude. The magnitude of $(x - y)$ is $n$ times the magnitude of $(x + y)$ . The angle between $x$ and $y$ is

The magnitude of vectors $O A$ , $O B$ , and $O C$ in the given figure are equal. The direction of $O A + O B - O C$ with X-axis will be

The angle between vector $A$ and $(A - B)$ is

A particle is moving Eastwards with a velocity of $5$ m/s. In $10$ s, the velocity changes to $5$ m/s Northwards. The average acceleration in this time is