First slide

Direction ratios and direction cosines

Question

The direction ratios of two lines are given by $a + b + c = 0, a^{2} + b^{2} - c^{2} = 0$ . Then $a (a + c) =$

Moderate

A

2
B

3
C

4
D

0

Solution

The given relations are
$a + b + c = 0 . . . . . . . . . . . . (1)$
$a^{2} + b^{2} - c^{2} = 0 . . . . . . . . . . . (2)$
From equation (2),
$\begin{matrix} a^{2} - c^{2} = - b^{2} \\ (a - c) (a + c) = - {(a + c)}^{2} \\ a - c = - a - c \\ 2 a = 0 \end{matrix}$
Hence, $a (a + c) = 0$

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