Question

Find the area of △ABC. Where:A=(3,2), B=(2,4), C=(0,2)

Suppose that a×b=〈−1,1,−1〉〉 and a⋅b=−4 Assume that θ is the angle between aand b. Find:

tanθ=

θ=

Find a nonzero vector orthogonal to both a=〈5,1,5〉, and b=〈2,−4,−1〉

Find a nonzero vector orthogonal to the plane through the points: A=(0,2,2), B=(−3,−2,2), C=(−3,2,3).

Find a nonzero vector orthogonal to the plane through the points: A=(0,1,−1), B=(0,6,−5), C=(4,−3,−4)..

Answer 1

Last problem is same just calculate a-b and a-c then take cross product between them which gives the required non zero orthogonal vector.

If you have any query you can ask me.