Question

if A= 3 I CAP + 2J CAP AND B= I CAP -2J CAP +3K CAP , THEN FIND THE MAGNITUDE OF A +B AND A-B

Answer 1

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CORRECT QUESTION :

$\sf \vec{A} \ = \ 3\hat{i} \ + \ 2\hat{j}$ and

$\sf \vec{B} \ = \hat{i} \ - \ 2\hat{j} \ + \ 3\hat{k}$. Then find the magnitude of A + B and A - B.

SOLUTION :

$\implies \sf \vec{a} \ + \vec{b} \ = \ 3\hat{i} \ + \ 2\hat{j} \ + \ \hat{i} \ - \ 2\hat{j} \ + \ 3\hat{k}$

$\implies \sf 4\hat{i} \ + \ 3\hat{k}$

Now,

Magnitude of $\sf \vec{A} \ + \ \vec{B} \ = \ \sqrt{4^{2}} \ + \ 3^{2}$

$\implies \sqrt{16 \ + \ 9}$

$\implies \sqrt{25}$

$\implies 25$

$\implies \sf \vec{a} \ + \vec{b} \ = \ 3\hat{i} \ + \ 2\hat{j} \ - \ \hat{i} \ - \ 2\hat{j} \ + \ 3\hat{k}$

$\implies \sf 2\hat{i} \ + \ 4\hat{j} \ - \ 3\hat{k}$

Now,

To find the magnitude of $\sf \vec{A} \ - \ \vec{B}$

$\implies \sf \vec{A} \ - \ \vec{B} \ = \ \sqrt 2^{2} \ + \ 4^{2} \ + \ (-3)^{2}$

$\implies \sf \sqrt {4 \ + \ 16 \ + \ 9}$

$\implies \sf \sqrt{29}$