University Of Johannesburg
Applied Mathematics 1A1E
Module Code: APM1EB1 || Year: 2026
Tutorial 9
1. Use properties of vector product to show that:
→
−
→
−
→
−
−
−
−
(a) (→
a + b ) × (→
a − b ) = −2(→
a × b)
→
−
→
−
→
−
−
−
−
(b) (2→
a − 3 b ) × (2→
a + 3 b ) = 12(→
a × b)
→
− −
−
c of the three vectors
2. Find the scalar triple product →
a · b ×→
→
−
→
−
−c = 5x̂ + ŷ − 3ẑ.
a = 2x̂ + 3ŷ + ẑ, b = x̂ − 2ŷ + 4ẑ, →
→
−
→
− −
−
−c = (2, −1, 0), compute →
−
3. If →
a = (1, 2, −1), b = (0, 1, 2), and →
a ×( b ×→
c ).
4. Consider a tetrahedron with equal side lengths. Suppose that three of its
vertices are (1, 1, 0), (1, 0, 1) and (0, 1, 1). Determine the position of the
fourth vertex.
1
0
