Find the image of the point having position vector `hat(i) + 3hat(j) + 4hat(k)` in the plane `vec(r ).(2hat(i) - hat(j) + hat(k))+ 3=0`

Find the image of the point having position vector hat i+2 hat j+4 hat k in the plane vec r.(2 hat i- hat j+ hat k)+3=0.

Find the projection of the vector vec(P) = 2hat(i) - 3hat(j) + 6 hat(k) on the vector vec(Q) = hat(i) + 2hat(j) + 2hat(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 angle between the vector vec(a) =2 hat(i) + 3hat(j) - 4 hat(k) and vec(b) = 4hat(i) +5 hat(j) - 2hat(k) .

Find the angle between the vectors 2 hat(i) - hat(j) - hat(k) and 3 hat(i) + 4 hat(j) - hat(k) .

Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector 2 hat i+3 hat j+4 hat k to the plane vec rdot(2 hat i+ hat j+3 hat k)-26=0. Also find image of P in the plane.

Find the unit vector of the vector vec(r ) = 4hat(i) - 2hat(j) + 3 hat(k)

Find the dot product of two vectors vec(A)=3hat(i)+2hat(j)-4hat(k) and vec(B)=2hat(i)-3hat(j)-6hat(k) .

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :