Let , and and be two vectors, such that and . Let , and be real numbers such that u =…

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let

\vec{w} = \hat{i} + \hat{j} - 2\hat{k}

, and

\vec{u}

and

\vec{v}

be two vectors, such that

\vec{u} \times \vec{v} = \vec{w}

and

\vec{v} \times \vec{w} = \vec{u}

. Let

\alpha, \beta, \gamma

, and

t

be real numbers such that

\vec{u} = \alpha\hat{i} + \beta\hat{j} + \gamma\hat{k}, \quad -t\alpha + \beta + \gamma = 0, \quad \alpha - t\beta + \gamma = 0, \quad \text{and} \quad \alpha + \beta - t\gamma = 0.

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I	List-II
(P) $\vec{v}^2$ is equal to	(1) 0
(Q) If $\alpha = \sqrt{3}$ , then $\gamma^2$ is equal to	(2) 1
(R) If $\alpha = \sqrt{3}$ , then $(\beta + \gamma)^2$ is equal to	(3) 2
(S) If $\alpha = \sqrt{2}$ , then $t + 3$ is equal to	(4) 3
	(5) 5

(A) (P)

\rightarrow

(2), (Q)

\rightarrow

(1), (R)

\rightarrow

(4), (S)

\rightarrow

(5) (B) (P)

\rightarrow

(2), (Q)

\rightarrow

(4), (R)

\rightarrow

(3), (S)

\rightarrow

(5) (C) (P)

\rightarrow

(2), (Q)

\rightarrow

(1), (R)

\rightarrow

(4), (S)

\rightarrow

(3) (D) (P)

\rightarrow

(5), (Q)

\rightarrow

(4), (R)

\rightarrow

(1), (S)

\rightarrow

(3)