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प्रश्न
An ant is moving along the vector `overset->l_1 = hati - 2hatj + 3hatk`. Few sugar crystals are kept along the vector `overset->l_2 = 3hati - 2hatj + hatk` which is inclined at an angle θ with the vector `overset->l_1`. Then find the angle θ. Also find the scalar projection of `overset->l_1 "on" overset->l_2`.
उत्तर
`theta = cos^-1 ((overset->l_1*overset->l_2)/(|overset->l_1|*|overset->l_2|))`
= `cos^-1 (((hati - 2hatj + 3hatk)*(3hati -2hatj + hatk))/(|(hati -2hatj + 3hatk)||(3hati - 2hatj + hatk)|))`
= `cos^-1 ((3 + 4 + 3)/(sqrt(1 + 4 + 9) sqrt(9 + 4 + 1)))`
= `cos^-1(10/14)`
= `cos^-1(5/7)`
Scalar projection of `overset->l_1 "on" overset->l_2 = (overset->l_1*overset->l_2)/(|overset->l_2|)`
= `((hati - 2hatj + 3hatk)*(3hati -2hatj + hatk))/(|(3hati - 2hatj + hatk)|`
= `(3 + 4 + 3)/(sqrt(9 + 4 + 1))`
= `10/sqrt14`
