Question

Let A=(1,2,3) , B(3, -1, 5) C=(4,0,-3). Then

• A. $\angle A={90}^{\circ }$
• B. $\angle B={90}^{\circ }$
• C. $\angle C={90}^{\circ }$
• D. $\angle A={45}^{\circ }$

Answer 1

The correct option is A $\angle A={90}^{\circ }$

$\overline{AB}=(3-1)\overline{i}+(-1-2)\overline{j}+(5-3)\overline{k}=2\overline{i}-3\overline{j}+2\overline{k}$

Similarly $\overline{BC}=\overline{i}+\overline{j}-8\hat{k}$

$\overline{CA}=-3\overline{i}+2\overline{j}+6\overline{k}$

$\overline{AB}\cdot \overline{BC}=2-3-16\ne 0$

$\overline{AB}\cdot \overline{CA}=-6-6+12=0$

$\therefore$ Angle between $\overline{AB}$ and $\overline{CA}$ is $0$

$\Rightarrow A={90}^o$.