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- Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and parallel to the plane x + y − z = 0.Two planes with equations x - y + 2z=4 and x + 2y - z = -5 intersect along a line L. Determine the distance from P(-1,2,-1) to L and determine the coordinates of the point on the L that gives the shortest distance.Compute the distance between the point (-2, 8, 1) and the line of intersection between the two planeshaving equations x+ y+ z=3 and 5x+ 2y+ 3z=8
- 2. Find an equation for a plane R at a distance 9 from a plane P with equation 2x + 2y - z = 3 .find an equation of the plane. The plane that passes through the point (1, −1, 1) and contains the line with symmetric equations x = 3y = 4zDetermine the distance from point Q = (2, 6, 9) to the plane x + 2y + 2z = 8
- The distance between the point (9, 8, 3) and the plane x + y−2z = 5 is _____.The lineL: x = 3 + 2t, y = 2t, z = tintersects the plane x + 3y - z = -4 in a point P. Find the coordinatesof P and find equations for the line in the plane through Pperpendicular to L.The distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is D = |d1 − d2| a2 + b2 + c2 . Find equations of the planes that are parallel to the plane x + 2y − 2z = −1 and three units away from it.