First slide

Direction ratios and direction cosines

Question

If $(3, - 1, 2), (4, 1, 0)$ are the direction ratios of two straight lines, then which of the following are not direction numbers perpendicular to both these lines?

Moderate

A

$〈- 2, 8, 7〉$
B

$〈2, - 8, - 7〉$
C

$〈- 32, 128, 112〉$
D

$〈32, 128, 112〉$

Solution

If $〈a_{1}, b_{1}, c_{1}〉, 〈a_{2}, b_{2}, c_{2}〉$ are direction ratios of two lines.
The direction ratios of any line perpendicular to the above two lines are proportional to the components of the vectors two whose direction ratios are $|\begin{matrix} i & j & k \\ a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \end{matrix}|$
Hence, $|\begin{matrix} i & j & k \\ a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \end{matrix}| = |\begin{matrix} i & j & k \\ 3 & - 1 & 2 \\ 4 & 1 & 0 \end{matrix}| = i (- 2) - j (- 8) + k (7)$
Therefore, the direction ratios of perpendicular line are proportional to $〈- 2, 8, 7〉$
It implies that $〈32, 128, 112〉$ are not proportional to the above direction ratios.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App