Vector Algebra Question 20

Question: The component of $\hat{i}+\hat{j}$ along $\hat{j}+\hat{k}$ will be

Options:

A) $\frac{\hat{i}+\hat{j}}{2}$

B) $\frac{\hat{j}+\hat{k}}{2}$

C) $\frac{\hat{k}+\hat{i}}{2}$

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ [ (\mathbf{i}+\mathbf{j}),.,\frac{(\mathbf{j}+\mathbf{k})}{\sqrt{2}} ]\frac{(\mathbf{j}+\mathbf{k})}{\sqrt{2}}=\frac{(\mathbf{j}+\mathbf{k})}{2}. $