Direction cosines and direction ratios

JEE Main Mathematics · 3D Geometry · 4 questions, latest first

• Let the direction cosines of two lines satisfy the equations: 4 l+m-n=0 and 2 mn+10 n l+3 l m=0. Then the cosine of the acute…202623 January, Shift 1 · Q16
• Each of the angles β and γ that a given line makes with the positive y - and z -axes, respectively, is half of the angle that…20253 April, Shift 2 · Q14
• A vector v in the first octant is inclined to the x -axis at 60^°, to the y -axis at 45^° and to the z -axis at an acute angle.…202330 January, Shift 2 · Q74
• Let a unit vector OP make angles α, β, γ with the positive directions of the co-ordinate axes OX, OY, OZ respectively, where β…202330 January, Shift 1 · Q76