Vectors Mock Tests

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

The volume of the parallelepiped formed by i+j, j+k, and k+i is:

The vector product (cross product) of two parallel vectors is:

The angle between the vectors a = i and b = i + j is:

The shortest distance between the lines r⃗ = (î + ĵ + k̂) + λ(î − ĵ + k̂) and r⃗ = (2î + ĵ + 3k̂) + μ(î − ĵ + k̂) is

The angle between the vectors a = i + j − k and b = 2i − j + 3k is:

If a⃗ = î + ĵ + k̂ and b⃗ = î − ĵ + k̂, then the projection of a⃗ on b⃗ is:

The volume of the tetrahedron with vertices at (1, 0, 0), (0, 2, 0), (0, 0, 3), and (0, 0, 0) is: