Fill in the blanks :
The equation of the line passing through (1, 2, 3) and parallel to `3hati-hatj+2hatk` is ……… .

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6.

State whether it is true or false The equation of line passing through (1, -1, 4) and parallel to (2hati+hatj-3hatk) is (x-2)/1=(y-1)/-1=(z+3)/4

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

Find the equation of the plane passing through (a, b, c) and parallel to the plane vecr cdot(hati + hatj + hatk) = 2

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3hati + 2hatj - 2hatk

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vecr cdot(hati+2hatj-5hatk) + 9 = 0

Find the value of equation of a line passing through the point (2,3,2) and parallel to the line vec r = ( - 2 hati + 3 hatj ) + lamda ( 2 hat i- 3 hatj + 6hatk). Also , find the distance between these two lines

Find the equation of the line passing through the point (1,2,-3) and perpendicular to the lines : vecr=(2hati-hatj-hatk)+lambda(2hati-hatj-3hatk) and vecr=(3hati-hatj-2hatk)+mu(hati+hatj+hatk)

Find the equation of the line passing through the point (1,-2,3) and perpendicular to the lines : vecr=(hati-2hatj+hatk)+lambda(hati+hatj+hatk) and vecr=(hati-hatj+2hatk)+mu(3hati-2hatj-5hatk)