Question

The co-ordinates of head and tail of a vector are $(2,1,0)$ and $(-4,2,-3)$ respectively . The magnitude of the vector is:

• A. $\sqrt{23}$ units
• B. $\sqrt{46}$ units
• C. $\sqrt{84}$ units
• D. $\sqrt{12}$ units

Answer 1

The correct option is B $\sqrt{46}$ units

Position Vector of head $=2\hat{i}+\hat{j}$
Position Vector of tail $=-4\hat{i}+2\hat{j}-3\hat{k}$
Vector $=(-4\hat{i}+2\hat{j}-3\hat{k})-(2\hat{i}+\hat{j})$ = $-6\hat{i}+\hat{j}-3\hat{k}$
$\therefore$ Magnitude of vector $=\sqrt{(-6{)}^2+1^2+(-3{)}^2}$$=\sqrt{46}$