Let \overrightarrow{w}=\hat{i}+\hat{j}-2 \hat{k}, and \overrightarrow{u} and \overrightarrow{v} be two vectors, such that \overrightarrow{u} \times \overrightarrow{v}=\overrightarrow{w} and \overrightarrow{v} \times \overrightarrow{w}=\overrightarrow{u}. Let \alpha, \beta, \gamma, and t be real numbers such that \overrightarrow{u}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k},-t \alpha+\beta+\gamma=0, \alpha-t \beta+\gamma=0, \text{ and } \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) |\overrightarrow{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 [JEE Adv 2025 P1]

Correct Answer is : (P) ⟶ (2) (Q) ⟶ (1) (R) ⟶ (4) (S) ⟶ (5)

(P) \rightarrow (2) (Q) \rightarrow (1) (R) \rightarrow (4) (S) \rightarrow (5)

(P) \rightarrow (2) (Q) \rightarrow (4) (R) \rightarrow (3) (S) \rightarrow (5)

( {\P}) \rightarrow(2)( {\Q}) \rightarrow(1)( {\R}) \rightarrow(4)( {\S}) \rightarrow(3)

(P) \rightarrow (5) (Q) \rightarrow (4) (R) \rightarrow (1) (S) \rightarrow (3)

Vector Algebra

Section: Mathematics

Question : 4 of 38

Marks: +1, -0

Let

→

∧

−2

∧

, and

→

and

→

be two vectors, such that

→

and

→

. Let α,β,γ, and t be real numbers such that

→

=α

∧

+β

∧

+γ

∧

,−tα+β+γ=0,α−tβ+γ=0,‌ and ‌α+β−tγ=0 Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I

List-II

(P)

→

|2 is equal to

(1)

(Q)

If α=√3, then γ2 is equal to

(2)

(R)

If α=√3, then (β+γ)2 is equal to

(3)

(S)

If α=√2, then t+3 is equal to

(4)

(5)

[JEE Adv 2025 P1]

(P) ⟶ (2) (Q) ⟶ (1) (R) ⟶ (4) (S) ⟶ (5)
(P) ⟶ (2) (Q) ⟶ (4) (R) ⟶ (3) (S) ⟶ (5)
(P)⟶(2)(Q)⟶(1)(R)⟶(4)(S)⟶(3)
(P) ⟶ (5) (Q) ⟶ (4) (R) ⟶ (1) (S) ⟶ (3)

Validate

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