Vectors Mock Tests

The scalar triple product [2a + b, a + 2b, a + b] where a and b are non-coplanar vectors with |a| = 1, |b| = 2, and a · b = 1 is:

If the vectors a = αî + 2ĵ + k̂, b = î − 2ĵ + k̂, and c = 2î + ĵ + 2k̂ are coplanar, then the value of α is

The equation of the line passing through the point (1, −1, 2) and parallel to the lines (x−2)/3 = (y+1)/4 = (z−2)/12 is

The three vectors i + j, j + k, and k + i are:

If a = 2i + j + k and b = i − j + 2k, then the scalar (dot) product a ⋅ b is:

The scalar product (dot product) of a → = 2i − j + 3k and b → = 3i + 2j + k is:

If a = 2i + j + k and b = i - j + k, then the projection of a on b is:

If a = 2i − j + 3k and b = i + 2j − k, then |a × b| equals: