Vectors A , B , and C are such A · B =0 A · C =0 . Then the vector parallel is A is:

Correct answer: C. B × C From vector produce A ×( B × C )=( B · C ) B -( A · B ) C Given that A · B =0, A · C =C then A ×( B × C )=0 thus vector A is paralles to B × C

NEET 2013

Exam: NEET
Year: 2013
Subject: Physics
Chapter: Mathematics in Physics

NEET 2013 · Physics · Mathematics in Physics

Vectors A , B , and C are such A · B =0 A · C =0 . Then the vector...

Vectors

\vec{A}, \vec{B}

, and

\vec{C}

are such

\vec{A} \cdot \vec{B}=0

\vec{A} \cdot \vec{C}=0

. Then the vector parallel is

\vec{A}

is:

Options

A $\vec{A} \times \vec{B}$
B $\vec{B} \times \vec{C}$
C $\vec{B} \times \vec{C}$
D $\vec{B}$ and $\vec{C}$

Correct answer

C. $\vec{B} \times \vec{C}$

Step-by-step solution

From vector produce

\vec{A} \times(\vec{B} \times \vec{C})=(\vec{B} \cdot \vec{C}) \vec{B}-(\vec{A} \cdot \vec{B}) \vec{C}

Given that

\vec{A} \cdot \vec{B}=0, \vec{A} \cdot \vec{C}=\mathrm{C}

then

\vec{A} \times(\vec{B} \times \vec{C})=0

thus vector

A

is paralles to

\vec{B} \times \vec{C}

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