Let a, b, c be unit vectors such that a+b+c=0 . Which one of the following is correct?

Correct answer: B. a × b=b × c=c × a ≠ 0 Since a, b, c are unit vectors and a+b+c=0 a, b and c represent an equilateral triangle. a × b=b × c=c × a ≠ 0 .

JEE Advanced 2007Paper 2

Exam: JEE Advanced
Year: 2007
Paper: Paper 2
Subject: Mathematics
Chapter: Vector Algebra

JEE Advanced 2007 · Paper 2 · Mathematics · Vector Algebra

Let a, b, c be unit vectors such that a+b+c=0 . Which one of the...

Let

\mathbf{a}, \mathbf{b}, \mathbf{c}

be unit vectors such that

\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}

. Which one of the following is correct?

Options

A $\mathbf{a} \times \mathbf{b}=\mathbf{b} \times \mathbf{c}=\mathbf{c} \times \mathbf{a}=\mathbf{0}$
B $\mathbf{a} \times \mathbf{b}=\mathbf{b} \times \mathbf{c}=\mathbf{c} \times \mathbf{a} \neq \mathbf{0}$
C $\mathbf{a} \times \mathbf{b}=\mathbf{b} \times \mathbf{c}=\mathbf{a} \times \mathbf{c}=\mathbf{0}$
D $\mathbf{a} \times \mathbf{b}, \mathbf{b} \times \mathbf{c}, \mathbf{c} \times \mathbf{a}$ are mutually perpendicular

Correct answer

B. $\mathbf{a} \times \mathbf{b}=\mathbf{b} \times \mathbf{c}=\mathbf{c} \times \mathbf{a} \neq \mathbf{0}$

Step-by-step solution

Since

\mathbf{a}, \mathbf{b}, \mathbf{c}

are unit vectors and

\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

represent an equilateral triangle.

\therefore \quad \mathbf{a} \times \mathbf{b}=\mathbf{b} \times \mathbf{c}=\mathbf{c} \times \mathbf{a} \neq \mathbf{0} .

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