1.

Find the scalar product of the following pairs of vectors and the angle between them. hati-hatj and hatj+hatk

Answer»

SOLUTION :Let `veca = hati-hatj, VECB = hatj+hatk`
Then `|veca| = sqrt2, |vecb| = sqrt2`
Now `veca.vecb = 1xx0-1xx1+0xx1 = 0-1+0 = -1`
if `theta` is the ANGLE between `veca` and `vecb` then
`theta = cos^(-1) ((veca.vecb)/(|veca||vecb|))`
=`cos^(-1)(-(1)/(sqrt2 sqrt2)) = cos^(-1) (-1/2) = (2pi)/3`.


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