Dot and Cross Products

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JEE Main 2021, 20 July Shift-I

If $A$ and $B$ are two vectors satisfying the relation $A \cdot B = ∣ A \times B ∣$ . Then, the value of $∣ A - B ∣$ will be

A^{2} + B^{2}

A^{2} + B^{2} + 2 A B

A^{2} + B^{2} + 2 A B

A^{2} + B^{2} - 2 A B

JEE Main 2021, 22 July Shift-II

What will be the projection of vector $A = \hat{i} + \hat{j} + \hat{k}$ on vector $B = \hat{i} + \hat{j}$ ?

2 (\hat{i} + \hat{j} + \hat{k})

2 (\hat{i} + \hat{j} + \hat{k})

2 (\hat{i} + \hat{j})

(\hat{i} + \hat{j})

JEE Main 2021, 22 July Shift-II

LEVELJEE Advanced

Three particles $P, Q$ and $R$ are moving along the vectors $A = \hat{i} + \hat{j}$ , $B = \hat{j} + \hat{k}$ and $C = - \hat{i} + \hat{j}$ , respectively. They strike on a point and start to move in different directions. Now, particle $P$ is moving normal to the plane which contain vectors $A$ and $B$ . Similarly, particle $Q$ is moving normal to the plane which contain vectors $A$ and $C$ . The angle between the direction of motion of $P$ and $Q$ is $cos^{- 1} (\frac{1}{x})$ . Then, the value of $x$ is ......... .

JEE Main 2019, 8 April Shift-II

Let $∣ A_{1} ∣ = 3, ∣ A_{2} ∣ = 5$ and $∣ A_{1} + A_{2} ∣ = 5$ . The value of $(2 A_{1} + 3 A_{2}) \cdot (3 A_{1} - 2 A_{2})$ is

- 106.5

- 112.5

- 99.5

- 118.5

If $A \times B = B \times A$ , then the angle between $A$ and $B$ is

π

π /3

π /2

π /4

JEE Main 2021, 25 Feb Shift-II

If $P \times Q = Q \times P$ , the angle between $P$ and $Q$ is $θ$ ( $0^{\circ} < θ < 36 0^{\circ}$ ). The value of $θ$ will be ……………