Vector Algebra PYQ — JEE Advanced 2025 · Shift 1 · Q32 with Solution

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

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

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

List – I	List – II
(P) $\lvert \vec{v} \rvert^2$ 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) $\to$ (2) (Q) $\to$ (1) (R) $\to$ (4) (S) $\to$ (5)
B
(P) $\to$ (2) (Q) $\to$ (4) (R) $\to$ (3) (S) $\to$ (5)
C
(P) $\to$ (2) (Q) $\to$ (1) (R) $\to$ (4) (S) $\to$ (3)
D
(P) $\to$ (5) (Q) $\to$ (4) (R) $\to$ (1) (S) $\to$ (3)

Vector Algebra question

Vector Algebra question

More from Vector Algebra

Vector Algebra question

Vector Algebra question

More from Vector Algebra