First slide

Direction ratios and direction cosines

Question

If $(x, 3, 5)$ and $(2, - 1, 2)$ are d.r’s of two lines and angle between the lines is $45^{0}$ then the values of x are

Moderate

A

$- 4, - 52$
B

3, 42
C

4, 52
D

-3, 32

Solution

$\cos θ = \frac{a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}}{\sqrt{{a_{1}}^{2} + {b_{1}}^{2} + {c_{1}}^{2}} \sqrt{{a_{2}}^{2} + {b_{2}}^{2} + {c_{2}}^{2}}} \frac{1}{\sqrt{2}} = \frac{2 x + 7}{3 \sqrt{34 + x^{2}}}$ $\Rightarrow x^{2} - 56 x + 208 = 0$ $\Rightarrow x = 4, 52$

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