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 a unit vector perpendicular to both the vector vec(a) = 2 hat(i) + hat(j) - 2 hat(k) and vec(b) = 3 hat (i) - hat (j) + hat (k)

Find the unit vector perpendicular to the plane vec r.(2 hat i+ hat j+2 hat k)=5.

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

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

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)

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

The , perpendicular vector on both of (3hat i +hat j + 2hat k) and (2hat i -2hat j +4hat k) is:

Find the vector alpha which is perpendicular to both 4 hat (i) + 5 hat (j) - hat (k) and hat (i) - 4 hat (j) + 5 hat (k) and which satisfies the relation alpha . beta = 21 where beta = 3 hat (i)+ 5 hat (j) - hat (k)

In each of the following cases two vectors are perpendicular to each other, find m m hat (i) - 2 hat (j) + hat(k) and 3 hat (i) - 2 hat (j) - 7 hat (k)

Find a vector in the direction of the vector 5 hat i - hat j + 2 hat k which has magnitude 8 units.