Question

The direction cosines of $\hat{i}$+$\hat{j}$+$\hat{k}$ are

• A. $1,1,1$
• B. $2,2,2$
• C. $1/\sqrt{2},1/\sqrt{2},1/\sqrt{2}$
• D. 1/$\sqrt{3},1/\sqrt{3},1/\sqrt{3}$

Answer 1

Answer: (D)

1/$\sqrt{3},1/\sqrt{3},1/\sqrt{3}$

Let $\overrightarrow{A}$ = $\hat{i}$+$\hat{j}$+$\hat{k}$

$\therefore$.$A_x$=1, $A_y$=1, $A_z$=1

$A=\sqrt{(A_x{)}^2+(A_y{)}^2+(A_z{)}^2}$ = $\sqrt{(1{)}^2+(1{)}^2+(1{)}^2}$ = $\sqrt{3}$

cos $\alpha$, cos $\beta$ and cos $\gamma$ are the direction cosines of $\overrightarrow{A}$.

$\therefore$ $cos\alpha =\frac{A_x}{|A|}=\frac{1}{\sqrt{3}}$, $cos\beta =\frac{A_y}{|A|}=\frac{1}{\sqrt{3}}$, cos$\gamma =\frac{A_z}{|A|}=\frac{1}{\sqrt{3}}$