Question: The two vectors 3i – 2j and 2i + 3j – 2k define a plane

Question: The two vectors 3i – 2j and 2i + 3j – 2k define a plane (it is the plane of the triangle with both tails at one vertex and each head at one of the other vertices). Which of the following vectors is perpendicular to the plane?

(1) 4i + 6j + 13k (2) -4i + 6j + 13k (3) 4i -6j + 13^k (4) 4i + 6j – 13k (5) 4i + 6j

Solution: You have to perform the cross product, use

then

i [(-2)(-2) -(0)(3)] – j[(3)(-2)-(0)(2)] + k [(3)(3) – (-2)(2)]

4i + 6j +13k

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