Find unit vector in which the direction of vector `vec a = 2 hat i + 3 hat j + hat k`.

Find the unit vector in the direction of vector vec(a)=2hat(i)+3hat(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) .

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) .

Find a unit vector in the direction of vec(A) = 3hat(i) - 2hat(j) + 6hat(k) .

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

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

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

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

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 ) .

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