If A→=2i^+3j^-k^ m and B→=i^+2j^+2k^ m. The magnitude of component of vector A→ along vector B→ will be _____ m.

Correct answer: 2. GIven vector are A→=2i^+3j^-k^ m and B→=i^+2j^+2k^ m Component of A→ along B→=A→·B^ =(A→·B→)/(B→)=2+6-2√(1^2+2^2+2^2)=6/3=2

Q81 / 90 · JEE Main 2022 (26 Jul Shift 2) · Physics

If $\vec{A} = (2 \hat{i} + 3 \hat{j} - \hat{k}) m$ and $\vec{B} = (\hat{i} + 2 \hat{j} + 2 \hat{k}) m$ . The magnitude of component of vector $\vec{A}$ along vector $\vec{B}$ will be _____ $m$ .

Correct answer: 2

Solution

GIven vector are $\vec{A} = (2 \hat{i} + 3 \hat{j} - \hat{k}) m$ and $\vec{B} = (\hat{i} + 2 \hat{j} + 2 \hat{k}) m$
Component of $\vec{A}$ along $\vec{B} = \vec{A} \cdot \hat{B}$
$= \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|} = \frac{2 + 6 - 2}{\sqrt{1^{2} + 2^{2} + 2^{2}}}$ $= \frac{6}{3} = 2$

Hence, the correct answer is 2.

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