Find the projection of the vector `hat(i)+3hat(j)+7hat(k)` on the vector `7hat(i)-hat(j)+8hat(k)`.

Explanation

`a=hat(i)+3hat(j)+7hat(k) and b=7hat(i)-hat(j)+8hat(k)`, then projection of `vec(a) on vec(b)` is
given by `(vec(a).vec(b))/(|b|)=(((hat(i)+3hat(j)+7hat(k)).(7hat(i)-hat(j)+8hat(k)))/(sqrt(7^2+(-1)^2+8^2)))=((1xx7+3xx(-1)+7xx8)/((sqrt(49+1+64))^2))=(7-3+56)/(sqrt(114))=(60)/(sqrt(114))`.
Hence, the projection of vector `(hat(i)+3hat(j)+7hat(k)) on (7hat(i)-hat(j)+8hat(k)) "is" (60)/(sqrt(114))`.