The position vector of the foot of theperpendicular from `(1,-2,-3)` to the line `bar r=bar i+bar j+lambda(2bar i+bar j+bar k)` is

Find the position vector of the centroid of the tetrahedron formed by the points 2bar(i)-bar(j)-3bar(k), 4bar(i)+bar(j)+3bar(k), 3bar(i)+2bar(j)-bar(k), bar(i)+4bar(j)+2bar(k) .

Find unit vector perpendicular to both bar(i) + bar(j) + bar(k) and 2bar(i) + bar(j) + 3bar(k) .

Write the position vector of the centroid of the triangle formed by the points whose position vectors are 3bar(i)+2bar(j)-bar(k), 2bar(i)-2bar(j)+5bar(k), bar(i)+3bar(j)-bar(k) .

The unit vector perpendicular to both of the vectors 2bar(i)-bar(j)+bar(k) and 3bar(i)+4bar(j)-bar(k) is.

A point on the line bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-2bar(j)+2bar(k)) is

Find the unit vector in the direction of the sum of the vectors bar(a) = 2bar(i)+ 2bar(j) - 5bar(k) and bar(b) = 2bar(i) + bar(j) + 3bar(k) .

Find a unit vector perpendicular to the plane containing the vector bar(a) = 4bar(i) + 3bar(j) - bar(k), bar(b) = 2bar(i) - 6bar(j) - 3bar(k)

Find the position vector of the point which divides the line joining the points bar(i)+bar(j)-4bar(k) and bar(i)+bar(j)+bar(k) in the ratio 3 : 2.