Question

If $A(0, 4, 1)$, $B(2, 3, -1)$, $C(4, 5, 0)$, then find the angle between the lines $AB$ and $BC$.

• A. $0^{\circ}$
• B. $30^{\circ}$
• C. $45^{\circ}$
• D. $90^{\circ}$

Answer 1

Answer: (D)

$d.r.'s$ of line $AB$ are $< 2 - 0$, $3 - 4$, $-1 - 1 >$
i.e., $< 2$, $-1$, $- 2 >$.
$d.r.'s$ of line $BC$ are $< 4 - 2$, $5 - 3$, $0 + 1 >$
i.e., $< 2$, $2$, $1 >$.
$\therefore cos\,\theta=\frac{\left(2\right)\left(2\right)+\left(-1\right)\left(2\right)+\left(-2\right)\left(1\right)}{\sqrt{4+1+4}\sqrt{4+4+1}}=0$
$\Rightarrow \theta=90^{\circ}$