Determice k so that the lines joining the points `p_1(k,1-,1)` and `P_2(2k,0,2)` shall be perpendicular to the line from `P_2` to `P_3(2+2k,k,1).`

Show by vector method that the line joining the points (1, 4, 2) and (-1, 1, -2) is perpendicular to the line joining the points (2,-3, 4) and (5, 3, -2) .

Show by vector method that the line joining the points (1, 4, 2) and (-1, 1, -2) is perpendicular to the line joining the points (2,-3, 4) and (5, 3,-2) .

Find the value of k if the points (k+1,1),(2k+1,3) and (2k+2,2k) are collinear.

Write the vector equation of the line passing through the point (1, 2, 3) and perpendicular to the plane r.(hat(i) + 2hat(j) - 5hat(k)) + 9 = 0 .

If the distance between the points (-1, -1, k) and (1,-1,1) is 2 then what is the value of k ?