Find the distance between the point with position vector ` hat i-5 hat j-10 hat k` and the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/(12)` with the plane `x-y+z=5.`

Find the distance between the point with position vector -hat i-5hat j-10hat k and the point of intersection of the line (x-2)/(3)=(y+1)/(4)=(z-2)/(12) with the plane x-y+z=5

Find the distance between the point with position vector -hat(i)-5hat(j)-10hat(k) and the point of intersection of the line (x-2)/(3)=(y+1)/(4)=(z-12)/(12) with the plane x-y+z=5 .

Find the distance between the points A and B with position vectors hat i-hat j and 2hat i+hat j+2hat k.

Find the distance of the point with position vector -hat i-5 hat j-10 hat k from the point of intersection of the line vec r=(2 hat i- hat j+2 hat k)+lambda(3 hat i+4 hat j+12 hat k) with the plane vec rdot(( hat i- hat j+ hat k)=5.

Find the distance of the point with position vector -hat i-5 hat j-10 hat k from the point of intersection of the line vec r=(2 hat i- hat j+2 hat k)+lambda(3 hat i+4 hat j+2 hat k) with the plane vec rdot(( hat i- hat j+ hat k)=5.

Find the equation of the line which passes through the point with position vector -hati + 2hat j + hat k and which is at right angles to each of the lines: (2x -1)/4 = (3 y + 5)/2 =(2 - z)/3 and x/-3 = y/2 = z/3 .

Find the equation of the line which passes through the point with position vector -hat(i)+2hat(j)+hat(k) and which is at right angles to each of the lines : (2x-1)/(4)=(3y+5)/(2)=(2-z)/(3)" and "(x)/(-3)=(y)/(2)=(z)/(5)

The angle between (hat i+hat j+hat k) and line of the intersection of the plane 2x+y+4z=0 and 3x+4y+z=0 is

Find the angle between the planes vec(r)*(hat(i)+hat(j)-2hat(k))=3and2x-2y+z=2

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.