JEE Main 202312 Apr, Morning shiftMathematicsHardVector Algebra184× since 2002Let λ∈Z,a⃗=λi^+j^−k^\lambda \in \mathbb{Z}, \vec{a}=\lambda \hat{i}+\hat{j}-\hat{k}λ∈Z,a=λi^+j^−k^ and b⃗=3i^−j^+2k^\vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}b=3i^−j^+2k^. Let c⃗\vec{c}c be a vector such that (a⃗+b⃗+c⃗)×c⃗=0→,a⃗⋅c⃗=−17(\vec{a}+\vec{b}+\vec{c}) \times \vec{c}=\overrightarrow{0}, \vec{a} \cdot \vec{c}=-17(a+b+c)×c=0,a⋅c=−17 and b⃗⋅c⃗=−20\vec{b} \cdot \vec{c}=-20b⋅c=−20. Then ∣c⃗×(λi^+j^+k^)∣2|\vec{c} \times(\lambda \hat{i}+\hat{j}+\hat{k})|^{2}∣c×(λi^+j^+k^)∣2 is equal to :AOption A. 53BOption B. 62COption C. 49DOption D. 46CheckSkip · show solution
