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.
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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 equal-magnitude denominators.
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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 two equations.
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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 derivation from the coplanarity condition.
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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 of three linear equations.