Q 11-03-123JEE MainJEE Main 2022 (28 Jul, Shift 1)Easy
If the projection of $2\hat i + 4\hat j - 2\hat k$ on $\hat i + 2\hat j + \alpha\hat k$ is zero. Then, the value of $\alpha$ will be ______ .
Numerical value type. Enter your answer.
Answer: 5
Zero projection means the dot product is zero:
$$(2)(1) + (4)(2) + (-2)(\alpha) = 0 \Rightarrow 10 - 2\alpha = 0 \Rightarrow \alpha = 5$$
Solution by Sreeraj P, M.Sc Physics