Write the direction cosines of the vector `2hat(i) + hat(j)- 5hat(k)`.

Find the direction cosines of vector, 2hat(i) + hat(j) + 3hat(k) .

Write the projection of the vector 7hat(i) + hat(j) - 4hat(k) on the vector 2hat(i) + 6hat(j) + 3hat(k) .

Write a vector in the direction of the vector hat(i) - 2hat(j) + 2hat(k) that has magnitude 9 units.

Write the projection of the vector hat(i) + hat(j) + hat(k) along the vector hat(j) .

Find a vector of magnitue 8 units in the direction of the vector, vec(a) = 5hat(i) - hat(j) + 2hat(k)

Write a unit vector in the direction of the sum of vectors vec(a) = 2hat(i) + 2hat(j) - 5hat(k) and vec(b) = 2hat(i) + hat(j) - 7hat(k) .

Write a vector of magnitude 15 units in the direction of vector hat(i) - 2hat(j) + 2hat(k) .

Obtain the projection of the vector vec(a) = 2hat(i) + 3hat(j) + 2hat(k) on the vector vec(b) = hat(i) + 2hat(j) + hat(k) .

Write a unit vector in the direction of the sum of vectors vec(a) = 2hat(i) - hat(j) + 2hat(k) and vec(b) = -hat(i) + hat(j) + 3hat(k) .

Find a vector in the direction of vector 2hat(i) - 3hat(j) + 6hat(k) which has magnitude 21 units.