JEE Main 20262 Apr, Evening shiftMathematicsMediumVector Algebra184× since 2002Let the vectors a⃗=−i^+j^+3k^\vec a=-\hat i+\hat j+3\hat ka=−i^+j^+3k^ and b⃗=i^+3j^+k^\vec b=\hat i+3\hat j+\hat kb=i^+3j^+k^. For some λ,μ∈R\lambda, \mu\in\mathbf{R}λ,μ∈R, let c⃗=λa⃗+μb⃗\vec c=\lambda\vec a+\mu\vec bc=λa+μb. If c⃗⋅(3i^−6j^+2k^)=10\vec c\cdot(3\hat i-6\hat j+2\hat k)=10c⋅(3i^−6j^+2k^)=10 and c⃗⋅(i^+j^+k^)=−2\vec c\cdot(\hat i+\hat j+\hat k)=-2c⋅(i^+j^+k^)=−2, then ∣c⃗∣2|\vec c|^2∣c∣2 is equal to :AOption A. 8BOption B. 12COption C. 14DOption D. 15CheckSkip · show solution
