The vectors `2i - 3j + k, I - 2j + 3k, 3i + j - 2k`

If the vectors 2i -- 3j + 4k, I + 2j - k, xi - j + 2k are coplanar then x = 8/5

If the vectors 2i - 3j + 4k, I + 2j - k and xi - j + 2k are coplanar then x =

A : The vector equation of the plane passing through I + j + k and parallel to the vectors 2i + 3j - k, I + 2j + 3k is [r - (I + j + k) 2i + 3j - k I + 2j + 3k] = 0 R : The vector equation of the plane passing through the point a and parallel to the vectors b,c is [r - a b c] = 0

If the three vectors 2i - j + k, I + 2j - 3k and 3i + lambda j + 5k are coplanar then lambda =

If vectors 2i - j + k, i + 2j - 3k and 3i + mj + 5k are coplanar, then m is a root of the equation

A : The vector equation of the plane passing through the point 2i + 2j - 3k and parallel to the vectors 3i + 3j - 5k, i + 2j + k is r = 2i + 2j - 3k + s(3i + 3j - 5k) + t(i + 2j + k) R : The vector equation of the plane passing through the points a, b, c is r = (1 - s - t) a + sb + tc

The volume of the parallelopiped whose coterminal edges are 2i - 3j + 4k, I + 2j - 2k, 3i - j + k is

If the position vectors of the vertices of a triangle are 2i - j + k, i - 3j - 5k, 3i - 4j - 4k then it is