Vectors Mock Tests

The vectors a⃗ = î + ĵ, b⃗ = 2î − ĵ + k̂, and c⃗ = 3î + λĵ + 2k̂ are coplanar if λ equals:

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

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

The volume of a tetrahedron with vertices at A(1, 1, 1), B(1, 2, 3), C(3, 1, 2), and D(2, 3, 1) is

The volume of the parallelepiped formed by vectors a, b, c is given by

The scalar product of â = 2î + ĵ − k̂ and b⃗ = î − 3ĵ + 2k̂ is:

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

The vector perpendicular to both i and j is: