Q69 / 160 · AP EAMCET 2024 (22 May Shift 1) · Mathematics

Let $\vec{a}=3 \hat{i}+4 \hat{j}-5 \hat{k}, \vec{b}=2 \hat{i}+\hat{j}-2 \hat{k}$. The projection of the sum of the vectors $\vec{a}, \vec{b}$ on the vector perpendicular to the plane of $\vec{a}, \vec{b}$ is

  • Correct answer
    A
    0
  • B
    $4 \sqrt{2}$
  • C
    $7 \sqrt{2}$
  • D
    $\frac{1}{\sqrt{2}}$

Solution

$\begin{aligned} & \text { Projection }=\frac{(\vec{a} \times \vec{b})}{|\vec{a} \times \vec{b}|} \cdot(\vec{a}+\vec{b}) \\ & =\frac{1}{|\vec{a} \times \vec{b}|}=0 \quad\left(\because\left[\begin{array}{lll}a & b & a\end{array}\right]+\left[\begin{array}{lll}a & b & b\end{array}\right]=0\right)\end{aligned}$

Hence, the correct answer is option: 'A'.

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