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If the position vectors of the points A, B, C be vector a, vector b, [3(vector a) - 2(vector b)] respectively, then the points A, B, C are?
Correct Answer Is : Collinear Let vector a, vector b, and vector c be three non-zero vectors, no two of which are collinear. If the [vector a + 2(vector b)] is collinear with vector c and [vector b + 3(vector c)] is collinear with vector a, then [vector a + 2(vector b) + 6(vector c)] is equal to ? Correct Answer Is : Zero vector Vector a and vector b are two non-collinear vectors, then [x(vector a) + y(vector b)] (where x and y are scalars) represents a vector which is? Correct Answer Is : Coplanar with vector a and vector b A, B, C, D, E are five coplanar points, then vector DA + vector DB + vector DC + vector AE + vector BE + vector CE = is equal to? Correct Answer Is : 3(vector DE) Area of the parallelogram whose diagonals are vector a and vector b is? Correct Answer Is : 1/2 |vector a * vector b| If vector a and vector b are unit vectors such that (vector a * vector b) is also a unit vector, then the angles between vector a and vector b is? Correct Answer Is : π/2 The number of vectors of unit length perpendicular to vectors vector a = (1, 1, 0) and vector b = (0, 1, 1) is? Correct Answer Is : Two If (vector a * vector b)^2 + [(vector a) . (Vector b)]^2 = 144 and |vector a| = 4, then |vector b| = ? Correct Answer Is : 3 [2(vector a) + 3(vector b)] * [5(vector a) + 7(vector b)] = ? Correct Answer Is : Vector b * vector a Let vector a, vector b, vector c be three vectors such that vector a ≠0, and [(vector a * vector b) = 2(vector a) * vector c], |vector a| = |vector c| = 1, |vector b| = 4 and |vector b * vector c| = √15. If [vector b - 2(vector c)] = λ (vector a), then λ is equal to? Correct Answer Is : ±4