Given unit vectors `hatm hatn and hatp` such that angle between `hatm and hatn is alpha` and angle between `hatp and hatm X hatn is alpha ` find alpha

Given unit vectors hatm hatn and hatp such that angle between hatm and hat n is alpha and angle between hatp and hatm X hatn is alpha if [n p m] = 1/4 find alpha

Let hata,vecb and vecc be the non-coplanar unit vectors. The angle between hatb and hatc is alpha "between" hatc and hata is beta and "between" hata and hatb is gamma . If A(hatacos alpha),B(hatbcosbeta) and C(hatc cosgamma), then show that in triangle ABC, (|hataxx(hatbxxhatca)|)/(sinA)=(|hatbxx(hatcxxhata)|)/sinB = (|hatcxx(hataxxhatb)|)/sinC=(prod|hataxx(hat xx hatc|))/(sumsin alpha-cosbeta. cos gammahatn_(1)) where hatn_(1)=(hatbxxhatc)/(|hatbxxhatc|),hatn_(2)=(hatcxxhata)/(|hatcxxhata|)and hatn_(3)=(hataxxhatb)/(|hataxxhatb|)

Let vecaxx(vecbxxvecc)=vecb/2 and vecb, vecc are non parallel unit vectors. If angle between veca and vecb is alpha and angle between veca and vecc is beta then |alpha-beta| is equal to (A) pi/2 (B) pi/6 (C) pi/3 (D) pi/4

If a and b are unit vectors and alpha is the angle between them , then a+b is unit vector when cos alpha =

The angle between the lines x cos alpha + y sin alpha = a and x sin beta - y cos alpha = a is

Angles between two lines alpha-beta

If hatl and hatm are unit vectors and theta is the angle between then theta is given by