Find the unit vector of `4hat(i)-3hat(j)+hat(k)`

The unit vectors parallel to the resultant vectors of 2hat(i)+4hat(j)-5hat(k) and hat(i)+2hat(j)+3hat(k) is

Find the magnitude of the vector (2hat(i) - 3hat(j) - 6hat(k)) + (-hat(i) + hat(j) + 4hat(k)) .

Find the value of lamda , if the points with position vectors 3hat(i)- 2hat(j)- hat(k), 2hat(i) + 3hat(j)- 4hat(k), -hat(i) + hat(j) + 2hat(k), 4hat(i) + 5hat(j) + lamda hat(k) are coplanar.

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

What is the value of b such that the scalar product of the vector hat(i)+hat(j)+hat(k) with the unit vector parallel to the sum of the vectors 2hat(i)+4hat(j)-5 hat(k) and b hat(i)+2hat(j)+3hat(k) is unity ?

Find a unit vector perpendicular to both the vectors 2 hat (i) - 3 hat (j) + 6 hat (k) and 3 hat (j) - 4 hat (k) . Also find the sine of the angle between the given vectors .

Find 'lambda' if the vectors : hat(i)-hat(j)+hat(k), 3hat(i)+hat(j)+2hat(k) and hat(i)+lambda hat(j)-3hat(k) are coplanar.