If a line makes the angle , , with three dimensional co-ordinate … - Vidyadip

MCQ

If a line makes the angle $\alpha ,\beta ,\gamma $ with three dimensional co-ordinate axes respectively, then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = $

A
$-2$
✓
$-1$
C
$1$
D
$2$

✓

Answer

Correct option: B.

$-1$

b
(b) $\cos \,2\alpha + \cos \,2\beta + \cos \,2\gamma $

$ = 2\,{\cos ^2}\alpha - 1 + 2\,{\cos ^2}\beta - 1 + 2\,{\cos ^2}\gamma - 1$

$ = 2\,({\cos ^2}\alpha + {\cos ^2}\beta + {\cos ^2}\gamma ) - 3 = 2 - 3 = - 1.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 11. three dimension geometry→STD 12 - 11. three dimension geometry — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int_{}^{} {\frac{1}{{{x^2}}}{{(2x + 1)}^3}} dx = $

The differential equation $\text{x}\frac{\text{dy}}{\text{dx}}-\text{y}=\text{x}^{2}$ has the general solution :

$\int\frac{1}{\cos\text{x}+\sqrt{3}\sin\text{x}}\text{ dx}$ is equal to:

The value of definite integral $\int\limits_\infty ^0 {\frac{{z\,{e^{ - z}}}}{{\sqrt {1 - {e^{ - 2z}}} }}\,dz} $.

An article manufactured by a company consists of two parts X and Y. In the process of manufacture of the part X. 9 out of 100 parts may be defective. Similarly 5 out of 100 are likely to be defective in part Y. Calculate the probability that the assembled product will not be defective.

If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by xRy ⇔ y = 3x, then R =

If $\text{A}=\begin{bmatrix} 3 & 4 \\ 2 & 4 \end{bmatrix},\text{B}=\begin{bmatrix} -2 & -2 \\ 0 & -1 \end{bmatrix}$ then $(A + B)^{-1} =$

On the interval $[0, 1],$ the function ${x^{25}}{(1 - x)^{75}}$ takes its maximum value at the point

Area bounded by parabola ${y^2} = x$ and straight line $2y = x$ is

Let $f(x) = \,\left\{ {\begin{array}{*{20}{c}} {\frac{{\sin \pi x}}{{5x}},}&{x \ne 0} \\ {k,}&{x = 0} \end{array}} \right.$ if $f(x)$ is continuous at $x = 0,$ then $k=$