Question

Let R = S x T and θ ≠ 90°, where θ is the angle between S and T when they are drawn with their tails at the same point. Which of the following is NOT true? a) - R = T x S b) ∣ R ∣=∣ S ∣∣ T ∣ sin ⁡ θ c) S . T = 0 d) R . S = 0 e) R . T = 0

Answer 1

The correct answer is:

c) S . T = 0

In the given options:

a) -R = T x S is true, as the cross product is anti-commutative, so T x S = -S x T = -R.

b) ∣R∣ = ∣S∣∣T∣sin(θ) is true, which is a formula for the magnitude of the cross product of vectors R, S, and T.

d) R . S = 0 is true because the dot product of two perpendicular vectors is always zero, and if θ ≠ 90°, then S and T are not perpendicular, so R and S are not perpendicular either.

e) R . T = 0 is also true because the dot product of R and T is zero for the same reason as d).

Therefore, the statement that is NOT true is c) S . T = 0.