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BITSAT 2012

Exam: BITSAT
Year: 2012
Subject: Mathematics
Chapter: Vector Algebra

BITSAT 2012 · Mathematics · Vector Algebra

If a .b =a .c and a × b=a × c , then correct statement is

If

a

.b

=a

.c and

a \times b=a \times c

, then correct statement is

Options

A $\mathrm{a} \|(\mathrm{b}-\mathrm{c})$
B $a \perp(b-c)$
C $a=0$ or $b=c$
DNone of these

Correct answer

C. $a=0$ or $b=c$

Step-by-step solution

a. b.=a \cdot c \Rightarrow a \cdot(b-c)=0\Rightarrow \mathrm{a}=0 \mathrm{or} \mathrm{b}-\mathrm{c}=0

or

\mathrm{a} \perp(\mathrm{b}-\mathrm{c})\Rightarrow \mathrm{a}=0

or

\mathrm{b}=\mathrm{c}

or

\mathrm{a} \perp(\mathrm{b}-\mathrm{c})

Also a

x b=a x c \Rightarrow a \times(b-c)=0\Rightarrow \mathrm{a}=0

or

\mathrm{b}-\mathrm{c}=0

or a

\|(\mathrm{b}-\mathrm{c})\Rightarrow a=0

or

b=c

or

a \|(b-c)

Observing to ( 1 ) and ( 2 ) we find that

\mathrm{a}=0

or

\mathrm{b}=\mathrm{c}

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