If the points `(1,1,p) a n d (3, "0, "1)` be equidistant from the plane ` vecr *(3 hat i+4 hat j-12 hat k)+13=0` , then find the value of p.

If the points (1,1,p) and (3,0,1) be equidistant from the plane vec r*(3hat i+4hat j-12hat k)+13=0, then find the value of p.

If the points (1,\ 1,\ lambda)a n d\ (-3,\ 0,\ 1) be equidistant from the plane vec rdot((3 hat i+4 hat j-12 hat k)+13=0 find the value of lambdadot

If the points (1,\ 1,\ lambda)a n d\ (-3,\ 0,\ 1) be equidistant from the plant vec rdot((3 hat i+4 hat j-12 hat k)+13=0 find the value of lambdadot

Show that the points hat i- hat j+3 hat ka n d3( hat i+ hat j+ hat k) are equidistant from the plane vec rdot(5 hat i+2 hat j+ hat k)+9=0 and lie on opposite sides of it.

Find the distance of a point (2, 5, 3) from the plane vecr.(6 hat i-3 hat j+2 hat k)=4 .

Find the distance of the point 2 hat i- hat j-4 hat k from the plane vec rdot((3 hat i-4 hat j+12 hat k)-9=0.

Find the distance of the point 2 hat i- hat j-4 hat k from the plane vec rdot((3 hat i-4 hat j+12 hat k)-9=0.

The distance of the point (1,-1,1) from vec(r)*(3 hat(i) - 4 hat(j)- 12 hat(k)) + 13 = 0 is

Show that the points hat i-hat j+3hat k and 3(hat i+hat j+hat k) are equidistant from the plane vec r*(5hat i+2hat j+hat k)+9=0 and lie on opposite sides of it.

The points hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k) are equidistant from the plane rcdot(5hat(i)+2hat(j)-7hat(k))+9=0 , then they are