The dot products of a vector with the vectors ` hat (i) - 3 hat(k) , hat (i) - 2hat (k) and hat (i) + hat (j)+ 4 hat (j) ` are 0,5,8 respectively . Find the vector .

The dot product of a vector with the vectors hat i-3 hatk,hat i-2 hatk and hat i+hat j+ 4 hat k are 0,5,8 respectively. Find the vector.

If the vectors 3 hat (i) - 2 hat (j) + m hat (k) and - 2 hat (i) + hat (j) +4 hat (k) are perpendicular to each other , find the value of m

For what values of p and q the vectors 2 hat (i) + p hat (j) - 3 hat (k) and q hat (i) - 4 hat (j) + 2 hat (k) are parallel ?

If the vectors x hat (i) - 4 hat (j) + 5 hat (k) , hat (i) + 2 hat (j) + hat (k) and2 hat (i) - hat (j) + hat (k) are coplanar , find the value x

Find the scalar and vector projections of 3 hat (i) - hat (j) + 4 hat (k) on 2 hat (i) + 3 hat (j) - 6 hat (k)

If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) and c hat (i) + c hat (j) + b hat (k) be coplanar, show that c^(2) = ab

The value of lamda for which the vectors vec(a) = hat(i) + 3hat(j) - hat(k) and hat(b) = 2hat(i) + 6hat(j) + lamda hat(k) are parallel is-

The scaler product of the vector hat (i) + hat (j) + hat (k) with the unit vector along the sum of vectors 2 hat (i) + 4 hat (j) - 5 hat (k) and lambda hat (i) + 2 hat (j) + 3 hat (k) is equal to one . Find the value of lambda

If vectors vec (a) = p hat (i) + 8 hat (j) + 6 hat (k) and vec (b) = - 3 hat (i) + 4 hat (j) + q hat (k) are parallel , find p and q

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 .