Home
Class 12
MATHS
If cos alpha, cos beta, cos gamma are th...

If `cos alpha, cos beta, cos gamma` are the direction cosines fo a vector `veca,` then `cos 2alpha + cos 2beta + cos 2gamma` is equal to

A

2

B

3

C

`-1`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

If a line makes angle alpha,beta,gamma with the axes respectively, then cos 2alpha+cos 2beta + cos 2gamma =

If alpha, beta, gamma are the angle made by a vector with the coordinate axes, then sin^(2) alpha + sin^(2) beta + sin^(2) gamma =

A line makes acute alpha, beta and gamma with the coordinate axes such that cos alpha . Cos beta = cos beta . Cos gamma = 2/9 and cos gamma . cos alpha = 4/9 , then cos alpha + cos beta + cos gamma =

Consider the equation 5 sin^2 x + 3 sin x cos x - 3 cos^2 x =2 .......... (i) sin^2 x - cos 2 x =2-sin 2 x ........... (ii) If tan alpha , tan beta satisfy (i) and cos gamma , cos delta satisfy (ii) , then tan alpha * tan beta + cos gamma + cos delta can be equal to

If alpha,beta,gamma are the roots of the equation 2x^(3) -3x^(2) +6x + 1 = 0 then alpha^(2) + beta^(2) + gamma^(2) is equal to…..

alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos^2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 cos alpha + cos beta + cos gamma can be equal to

Evaluate {:|( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) |:} =1

Prove that if cos alpha ne 1, cos beta ne1 and cos gamma ne 1 , then the vectors a=hati cos alpha+hatj+hatk,b=hati+hatj cos beta+hatk and c=hati+hatj+hatk cos gamma can never be coplanar.

If alpha, beta, gamma are the roots of x^3+a x^2+b=0 then the value of [[alpha , beta , gamma],[beta , gamma , alpha],[gamma , alpha , beta]] is