If a unit vector `vec(a)` makes an angle `(pi)/(3)` with `hat(i), (pi)/(4)` with `hat(j)` and a acute angle `theta` with `hat(k)`, then find the value of `theta`.

If a unit vector hat(a) , makes angles (pi)/(3) with hat(i),(pi)/(4) with hat(j) and an acute angle theta with hat(k) , then find theta and hence the components of a.

If a unit vector veca makes angles (pi)/(3) with hati,(pi)/(4) with hatj and an acute angle theta with hatk then find theta and hence , the components of veca .

let vec a= ( hat i+ hat j+ hat k) then find the unit vector along this vector

If vec(AB) = 3hat(i) + 2hat(j) + 6hat(k), vec(OA) = hat(i) - hat(j) - 3hat(k) , find the value of vec(OB) .

The scalar product of the vector vec(a) = hat(i) + hat(j) + hat(k) with a unit vector along the sum of vectors vec(b) = 2hat(i) + 4hat(j) - 5hat(k) and vec(c ) = lambda hat(i) + 2hat(j) + 3hat(k) is equal to one. Find the value of lambda and hence find the unit vector along vec(b) + vec(c ) .

The unit vector perpendicular to the vectors hat(i) -hat(j) + hat(k), 2hat(i) + 3hat(j) -hat(k) is

If the position vectors of vec(A) and vec(B) are 3hat(i) - 2hat(j) + hat(k) and 2hat(i) + 4hat(j) - 3hat(k) the length of vec(AB) is

If vec(a) = x hat(i) + 2hat(j) - zhat(k) and vec(b) = 3hat(i) - y hat(j) + hat(k) are two equal vectors, then write the value of x+y+z.

If a hat(i) + 6hat(j) - hat(k) and 7hat(i) -3hat(j) + 17hat(k) are perpendicular vectors, then the value of a= ….