Find the co-ordinates of the foot of perpendicular and length of perpendicular drawn from point `(hati+6hatj+3hatk)` to the line `vecr = hatj+2hatk+lambda(hati+2hatj+3hatk)`.

Find the co ordinates of the foot of perpendicular and the length of the perpendicular drawn from the point P(5,4,2) to the line : vecr=-hati+3hatj+hatk+lambda(2hati+3hatj-hatk) . Also find the image of P in this line.

Find the coordinates of the foot of the perpendicular and the length of the perpendicular drawn from the point P(5,4,2) to the line vecr=(-hati+hatj+hatk)+lambda(2hati+hatj-hatk) . Also find the image of P in this line.

Find the perpendicular distance from the point (1,2,3) to the line : vecr=6hati+7hatj+7hatk+lambda(3hati+2hatj-2hatk)

The position vector of the foot of the perpendicular draw from the point 2hati-hatj+5hatk to the line vecr=(11hati-2hatj-8hatk)+lamda(10hati-4hatj-11hatk) is

The position vector of the foot of the perpendicular draw from the point 2hati-hatj+5hatk to the line vecr=(11hati-2hatj-8hatk)+lamda(10hati-4hatj-11hatk) is

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

The shortest distance between the lines vecr = (2hati - hatj) + lambda(2hati + hatj - 3hatk) vecr = (hati - hatj + 2hatk) + lambda(2hati + hatj - 5hatk)