Find the length of the perpendicular drawn from the point (5, 4, -1) to the line `vecr=hati+lamda(2hati+9hatj+5hatk)`, where `lamda` is a parameter.

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 length and the foot of perpendicular drawn from the point (1,1,2) to the plane vecr.(2hati-2hatj+4hatk)+5=0 .

The length of perpendicular from the origin to the line vecr=(4hati+2hatj+4hatk)+lamda(3hati+4hatj-5hatk) 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

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 coordinates of the foot of perpendicular drawn from the point 2hati - hatj + hat5k to the line bar(r) = (11hati + 2hatj - 8hatk) + lamda ( 10 hati - 4hatj - 11hatk) . Also , find the length of perpendicular .

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) .