[" If "alpha,beta,gamma" are the direction angles of a vector."],[" and "cos alpha=(14)/(15),cos beta=(1)/(3)," then cos "gamma=]

If alpha,beta ,gamma are direction angles of a line , then cos 2alpha + cos 2beta + cos 2 gamma =

If alpha,beta,gamma are direction - angles of a line prove that cos2 alpha+cos2beta+cos2gamma=-1

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled

If alpha,beta, gamma are any three angles , then cos alpha + cos beta - cos gamma - cos (alpha+beta+gamma)=

If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),cos (gamma-beta),1)] then which of following is/are true ?

If alpha,beta,gamma are three real numbers and A=[(1,"cos"(alpha-beta),"cos"(alpha-gamma)),(cos(beta-alpha),1,"cos"(beta-gamma)),("cos"(gamma-alpha),"cos"(gamma-beta),1)] , then which of following is/are true? a. A is singular b. A is symmetric c. A is orthogonal d. A is not invertible

If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),cos (gamma-beta),1)] then which of following is/are true ?