Can a vector have direction angles `45^0,60^0,120^0`

If a vector has direction angles 45^(@) and 60^(@) find the third direction angle.

Can a line make angle 45^(@), 60^(@), 120^(@) with x-,y- and z-axes respectively.

The unit vector in XOZ plane and making angles 45^(@) and 60^(@) respectively with vec a=2i+2j-k and vec b=0i+j-k, is

A line making angles 45^0 and 60^0 with the positive directions of the x and y axes respectively , makes with the positive direction of z-axis an angle of (A) 60^0 (B) 120^0 (C) 60^0 or 120^0 (D) none of these

Find a unit vector in XY plane which makes an angle 45^(@) with the vector hati + hatj at angle of 60^(@) with the vector 3 hati - 4 hatj.

In an isosceles triangle,if the vertex angle is twice the sum of the base angles,then the measure of vertex angle of the triangle is 100^(0) (b) 120^(0) (c) 110^(0) (d) 130^(0)

If a vector vecA makes angles 45^(@) and 60^(@) with x and y axis respectively then the angle made by it with z-axis is

Let a vector a hati + beta hatj be obtained by rotating the vector sqrt3 hati + hatj by an angle 45^(@) about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having vertices (alpha, beta) , (0, beta) and (0,0) is equal to:

Unit vector in the xyplane that makes and angle of 45^0 with the vector hati+hatj and an angle of 60^0 with the vector 3hati-4hatj is (A) hati (B) (hati+hatj)/sqrt(2) (C) (hati-hatj)/sqrt(2) (D) none of these

In each of the following,the measures of three angles are given.State in which cases,the angles can possibly be those of a triangle: 63^(0),37^(0),80^(0) (ii) 45^(@),61^(0),73^(0)59^(0),72^(0),61^(0)( iv )45^(0),45^(0),90^(0)30^(0),20^(0),125^(0)