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Find the unit vector coplanar with i+j+2k and i+2j+k and perpendicular to i+j+k.?
Let the required vector is xa + yb r = x(i + j +2k) + y (i + 2j + k) = (X+y)i + (x+2y)j + (2x + y)k Now it should be perpendicular to i + j + k Hencer . (i+j+k) = 0 x+y + 2x + y + x +2y = 0 x+ y = 0 Nowr should be a unit vector hencesqrt((x+y)² +(x+2y)² + (2x+y)²) = 1 Solve both the equations r will come out as r = +- (j+k)/sqrt(2)
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