1. If = 2i - 3j + 5k and = i - 4j + 2k then find A × B.
Sol: Given = 2i - 3j + 5k
= i - 4j + 2k
× = i(-6 + 20) - j(4 - 5) + k(-8 + 3)
× = 14i + j - 5k
2. Find the unit vector perpendicular to both vectors 2i + j + 3k and i - 2j + k.
Sol: Given vectors = 2i + j + 3k; = i - 2j + k
5. Find Sine of the angle between the two vectors 2i - j + k and 3i + 4j - k.
6. Find the area of the parallelogram with adjacent sides - i + k and 2j - k.
8. If (1, 2, 3), (2, 5, -1) and (-1, 1, 2) are the vertices of triangle then find its area.
12. Find the cartesian equation of the plane passing through the points (1, 2, 3), (2, - 3, 1) (3, 1, - 2)
Sol: Given Points (x1, y1, z1) = (1, 2, 3)
(x2, y2, z2) = (2, - 3, 1)
(x3, y3, z3) = (3, 1, - 2)
( x - 1 )( 25 - 2 ) - ( y - 2 )( -5 + 4 ) + ( z - 3 ) ( -1 + 10 ) = 0
23x - 23 + y - 2 + 9z - 27 = 0
23x + y + 9z - 52 = 0
Writer Sayyad Anwar