vector

Show that the points A(4, 5, 2), B(3, 2, 4) and C(5, 8, 0) are collinear.

If A(5, 1, p), B(1, q, p), and C(1, -2, 3) are vertices of a triangle and G(r , -4/3 , 1/3) is its centroid, then find the values of p, q, r by vector method.

If line makes angles 90, 135°, 45° with X, Y, and Z axes respectively, then find its direction cosines.

Find the direction cosines of the vector 2i + 2j- k

Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are -2, 1, -1 and -3, -4, 1.

If c=3a-2b, then prove that [a b c] = 0.