JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q12

← JEE Main 2022 · 27 Jul · Shift 1

MathematicsSingle correct+4 / -1Question 12 of 90

Let $\vec a=\alpha\hat i+\hat j+\beta\hat k$ and $\vec b=3\hat i-5\hat j+4\hat k$ be two vectors, such that $\vec a\times\vec b=-\hat i+9\hat j+12\hat k$ . Then the projection of $\vec b-2\vec a$ on $\vec b+\vec a$ is equal to

\dfrac{39}5

\dfrac{46}5

Answer and worked solution

Official answer: Dropped: full marks to everyone

This question was dropped in NTA's final key.

As printed. $\vec a\times\vec b=(4+5\beta,\,3\beta-4\alpha,\,-5\alpha-3)=(-1,9,12)$ gives $\beta=-1$ , $\alpha=-3$ . Then $\vec b-2\vec a=(9,-7,6)$ and $\vec b+\vec a=(0,-4,3)$ , so the projection is $\frac{46}5$ , which is option (D).

Topics:Cross product Dot product

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 12