If the perpendicular distance of the plane passing through the point Q(1, 0, -1) and containing the line r = ( i - 3 j + k ) + (2 i - 2 j + k ) from origin is p 53 then p = ...

Step-by-step solution

The plane contains the point Q(1, 0, -1) and the line r = ( i - 3 j + k ) + (2 i - 2 j + k ) . The line passes through the point A(1, -3, 1) and has the direction vector b = 2 i - 2 j + k . Since the plane contains both the point Q and the line, it contains the vector QA joining Q and A . QA = (1 - 1) i + (-3 - 0) j + (1 - (-1)) k = -3 j + 2 k The normal vector n to the plane is perpendicular to both b and QA . n = b QA = vmatrix i & j & k 2 & -2 & 1 0 & -3 & 2 vmatrix n = i (-4 - (-3)) - j (4 - 0) + k (-6 - 0) = -