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Question

Physics Question on Vector basics

Give P⃗=2i^−3j^+4k^\vec{P} = 2 \hat{i} - 3 \hat{j} + 4 \hat {k} and Q⃗=j^−2k^\vec{Q} = \hat{j} - 2 \hat {k} The magnitude of their resultant is.

A

3\sqrt {3}

B

232\sqrt {3}

C

333 \sqrt {3}

D

434\sqrt{3}

Answer

232\sqrt {3}

Explanation

Solution

∣P⃗+Q⃗∣=∣2i^−3j^+4k^+j^−2k^∣|\vec{P}+\vec{Q}|=|2 \hat{i}-3 \hat{j}+4 \hat{k}+\hat{j}-2 \hat{k}|
=∣2i−2j^+2k^∣= |2 i-2 \hat{j}+2 \hat{k}|
=22+22+22=23=\sqrt{2^{2}+2^{2}+2^{2}}=2 \sqrt{3}