Scalar and Vector Quantities

Interactive Feed

The non-zero vectors are $a, b$ and $c$ are related by $a = 8 b$ and $c = - 7 b$ . Then the angle between $a$ and $c$ is

π /4

π /2

π

ABC is a triangle, right angled at A. The resultant of the forces acting along $A B, B C$ with magnitudes $\frac{1}{A B}$ and $\frac{1}{A C}$ respectively is the force along $A D$ , where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is

\frac{A B ^{2} + A C ^{2}}{( A B ) ^{2} ( A C ) ^{2}}

\frac{( A B ) ( A C )}{A B + A C}

\frac{1}{A B} + \frac{1}{A C}

\frac{1}{A D}

A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/hr. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively

\frac{13}{9}

\frac{17}{9}

\frac{13}{4}

\frac{17}{4}

\frac{17}{9}

\frac{13}{9}

\frac{17}{4}

\frac{13}{4}

JEE Main 2024 (27 Jan Shift 2)

Let the position vectors of the vertices $A, B$ and $C$ of a triangle be $2 \hat{i} + 2 \hat{j} + \hat{k}$ , $\hat{i} + 2 \hat{j} + 2 \hat{k}$ and $2 \hat{i} + \hat{j} + 2 \hat{k}$ respectively. Let $l_{1}, l_{2}$ and $l_{3}$ be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides $A B, B C$ and $C A$ respectively, then $l_{1}^{2} + l_{2}^{2} + l_{3}^{2}$ equals:

\frac{1}{5}

\frac{1}{2}

\frac{1}{4}

\frac{1}{3}

JEE Main 2024 (29 Jan Shift 1)

Let $a, b$ and $c$ be three non-zero vectors such that $b$ and $c$ are non-collinear if $a + 5 b$ is collinear with $c$ , $b + 6 c$ is collinear with $a$ and $a + α b + β c = 0$ , then $α + β$ is equal to