Find the value of `x` for which `x\ ( hat i+ hat j+ hat k)` is a unit vector.

Write the value of p for which the vectors 3hat(i) + 2hat(j) + 9hat(k) and hat(i) - 2p hat(j) + 3hat(k) are parallel vectors.

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 ) .

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

Find the value of lambda if the vectors vec(a) = 3hat(i) + hat(j) - 2hat(k) and vec(b) = hat(i) + lambda hat(j) - 3hat(k) are perpendicular to each other.

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

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) .

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) .

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