Vectors Vector Algebra Mock Tests

Let a = (1, 1, 1), b = (1, -1, 1), and c = (alpha, beta, gamma) be three vectors. If a . c = 4 and c is perpendicular to b, then which of the following is/are TRUE?

If a = i + j, b = j + k, and c = k + i, then the scalar triple product [a b c] equals:

Let a = i + j + k. If a vector r = 2i + j satisfies a x r = b, then b is

Let a, b, c be three non-coplanar vectors. Let p = a x b + b x c + c x a and q = (b - c) x (c - a). If p . (a + b + c) = 30, then q . (a + b + c) equals:

Let a = (1,1,1) and b = (1,-1,1). If c is coplanar with a and b and c is perpendicular to a, then c can be:

Let a = i + j, b = j + k, and c = k + i. The scalar triple product [a b c] is equal to:

Let a = i + j + k and b = i - k. A vector r such that a x r = b and a . r = 1 is

Let a = i + j, b = j + k, and c = 2i + kj. For what value of k are the vectors a, b, and c coplanar?