(c) In option (a) (A. A) (B. C) (A2)(BCcosθ) =A2BCcosθ Scalar value In option (b) (A×B)(B×C)=(ABsinθ
∧
n
)⋅(BCsinφk) =(ABsin(θ)(BCsinφ)(
∧
n
⋅
∧
k
) where,
∧
n
is unit vector perpendicular to both vector A and B and hatk is unit vector perpendicular to both vector B and C. ∴
∧
n
⋅k= scalar value ∴(A×C)⋅(B×C) is a scalar value In option (c) (A×C)×(B×C)=(ACsinθ1)
∧
r
×(BCsinθ2)
∧
r
2.. =(ACsinθ1)(BCsinθ2)(
∧
r
×
∧
r
2)
∧
r
1×
∧
r
2 is a vector product, hence it gives a vector value. Therefore, (A×C)×(B×C) is a vector value. In option (d) A×(B×C) is vector triple product which gives a vector value.
