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Find the unit vector parallel to the dia...

Find the unit vector parallel to the diagonal of the parallelogram whose adjacent sides given by the vectors `2i -4j +5k` and`i+2 j-3k`. Also find its area:

Text Solution

Verified by Experts

Here, `vec(a) = 2hati-4hatj+5hatk`
`vec(b) = hati-2hatj-3hatk`
Area = `|vec(a)xxvec(b)|`
`vec(a)xxvec(b) = 22hati+11hatj ` (Please see video for computation)
So, Area = `sqrt(22^2+11^2) = sqrt605 = 11sqrt5`
`vec(a)+vec(b) = 3hati-6hatj+2hatk`
Unit vector parallel to diagonal can be given as:
`3hati-6hatj+2hatk/sqrt(3^2+6^2+2^2) = (3hati-6hatj+2hatk)/7 `
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