Question

5. If vector A= 3i+4j+k and
vector B=i-j-k determine the
magnitude of A+B *
O Root 5
O Root 4
O 5
06​

Answer 1

Answer:

5

Explanation:

Given,

A = $\sf 3\hat{i}+4\hat{j}+\hat{k}$

B = $\sf \hat{i}-\hat{j}-\hat{k}$

To Find :-

Magnitude of A+B.[|A+B|]

Solution :-

First let's find the value of A+B :-

A + B = $\sf 3\hat{i}+4\hat{j}+\hat{k}+(\hat{i}-\hat{j}-\hat{k})$

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

= $\sf 3\hat{i}+\hat{i} + 4\hat{j}-\hat{j}+/hat{k}-\hat{k}$

= $\sf 4\hat{i}+3\hat{j}$

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

= $\sf\sqrt{16+9}$

= $\sf\sqrt{25}$

= 5

Magnitude of A+B = |A+B| = 5

Hence option 'C' = 5.