Vectors and 3D Geometry
5 solved problems from JEE previous year papers.
Vector Algebra
Vector d Perpendicular to Both a and b, With c·d=15
Given a=i+4j+2k, b=3i−2j+7k, c=2i−j+4k, find vector d perpendicular to both a and b with c·d=15, using the cross product a×b.
Three Dimensional Geometry
Direction Cosines of the Line 5x−3=15y+7=3−10z
Find the direction cosines of 5x−3=15y+7=3−10z and a point through which it passes, by converting to symmetric form with…
Vector Algebra
If 3a+2b=5c and 8a−7b=4c, Are a,b,c Collinear and Is |a|>|b|?
Given 3a+2b=5c and 8a−7b=4c, determine whether |a|>|b| and whether a, b, c are collinear vectors, by eliminating c between the…
Vector Algebra
Four Coplanar Points With Position Vectors a,b,c,d, Which Identity Holds
If four distinct points with position vectors a,b,c,d are coplanar, which scalar triple product identity must hold? A worked…
Vector Algebra
Find Vector d Perpendicular to Both b and c, With d·a = 21
Given vectors a=4i+5j−k, b=i−4j+5k, c=3i+j−k, find vector d perpendicular to both b and c such that d·a=21, by solving a system…