Let `P(3, 2, 6)` be a point in space and Q be a point on line `vecr= (hati-hatj+2hatk)+mu (-3hati+hatj+ 5hatk)`. Then the value of `mu` for which the vector `vec(PQ)` is parallel to the plane `x-4y+ 3z=1` is

Let A be a point on the line vec(r)=(1-3mu)hati+(mu-1)hatj+(2+5mu)hatk and B(3,2,6) be a point in the space. Then the value of mu for which the vector vec(AB) is parallel to the plane x-4y+3z=1 is: (a) 1/8 (b) 1/2 (c) 1/4 (d) -1/4

Let A be a point on the line vecr = (1- 5 mu) hati + (3mu - 1) hatj + (5 + 7mu )hatk and B (8, 2, 6) be a point in the space. Then the value of mu for which the vector vec(AB) is parallel to the plane x - 4y + 3z = 1 is:

Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) and the plane vecr.(3hati+2hatj-hatk)=4 is

Find the points of intersection of the line vecr = (2hati - hatj + 2hatk) + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

Find the angle between the line vecr = (2hati+hatj-hatk)+lambda(2hati+2hatj+hatk) and the plane vecr.(6hati-3hatj+2hatk)+1=0 .

The vector equation of the plane containing he line vecr=(-2hati-3hatj+4hatk)+lamda(3hati-2hatj-hatk) and the point hati+2hatj+3hatk is

Find the mid point of the line segment joining the points P(2hati+3hatj+3hatk) and Q(4hati+hatj-2hatk)

Find the line of intersection of the planes vecr.(3hati-hatj+hatk)=1 and vecr.(hati+4hatj-2hatk)=2

Vector equation of the plane r = hati-hatj+ lamda(hati +hatj+hatk)+mu(hati – 2hatj+3hatk) in the scalar dot product form is

Convert the equation of the plane vecr = (hati-hatj)+lambda(-hati+hatj+2hatk)+mu(hati+2hatj+hatk) into scalar product form.