Vectors A→ , B→ and C→ are such that A→

Home » Mechanics » Motion in a Plane » Question

Vectors A^{^→} , B^{^→} and C^{^→} are such that A^{^→} . B^{^→} = 0 and A^{^→} . C^{^→} = 0 Then the vector parallel to A^{^→} is

1. B^{^→} and C^{^→}
2. A^{^→} × B^{^→}
3. B^{^→} . C^{^→}
4. B^{^→} × C^{^→}

Correct Option: D

Vector triple product
A^{^→} × (B^{^→} × C^{^→}) = B^{^→}(A^{^→} . C^{^→}) - C^{^→}(A^{^→} . B^{^→}) = 0
⇒ A^{^→} || (B^{^→} × C^{^→})
[ ∵ A^{^→} . B^{^→} = 0 and A^{^→} . C^{^→} = 0 ]
(A^{^→} + B^{^→})² = (C^{^→})²
⇒ A^{^→}² + B^{^→}² + 2A^{^→} . B^{^→} = C²
⇒ 3² + 4² + 2A^{^→} . B^{^→} = 5²
⇒ 2A^{^→} . B^{^→} = 0
or ⇒ A^{^→} . B^{^→} = 0
∴ A^{^→} ⊥ B^{^→}
Hence A² + B² = C² . Hence A^{^→} ⊥ B^{^→}