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Question

Given two vectors a=ˆi+ˆj+2ˆk and b=ˆi2ˆjˆk.

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Solution

a. a×b=∣ ∣ ∣ˆiˆjˆk112121∣ ∣ ∣=3ˆi3ˆj+3ˆk
Hence, the area of the triangle is 332.
b. The area of the parallelogram is 33
c. The area of a parallelogram whose diagonals are 2a and 4b is 12|2a×4b|=123
d. Volume of the parallelepiped
=|(a×b)c|=9+36+9=36

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