A- 0- a-b - a-c-b - c nbsp-TrueFalse

The correct option is B FalseIt is given that a≠ 0 and a×b = a×c a×b = a×c can be written as a× (b c) = 0 Now cross product of two vectors is zero when nb ...

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Byju's Answer

Standard IX

Mathematics

Cross Product of Two Vectors

a≠ 0, a×b = a...

Question

$\to a \neq 0, \to a \times \to b = \to a \times \to c \Rightarrow \to b = \to c$

True

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False

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Solution

The correct option is B False
It is given that $\to a \neq 0$ and $\to a \times \to b = \to a \times \to c$
$\to a \times \to b$ = $\to a \times \to c$ can be written as $\to a \times (\to b - \to c) = \to 0$
Now cross product of two vectors is zero when
1) Either of the two or both vectors are zero
Or
2) They are parallel to each other.
It is given that $\to a \neq 0$
So
either $\to a$ is parallel to $\to b - \to c$
or $\to b - \to c$ = 0 i.e., $\to b = \to c$

So $\to a \times \to b = \to a \times \to c$ will imply following
Either $\to b = \to c$
or $\to a$ is parallel to $\to b - \to c$

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Similar questions

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(a) a + b + c = 0

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(c) a + b + c = 3abc

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|\begin{matrix} b + c & c + a & a + b \\ c + a & a + b & b + c \\ a + b & b + c & c + a \end{matrix}| = 0

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Q. If

\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c}

and

\vec{a} \times \vec{b} = \vec{a} \times \vec{c,} \vec{a} \neq 0,

then
(a)

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(b)

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(c)

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(d) none of these

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→a≠0,→a×→b=→a×→c⇒→b=→c

$\to a \neq 0, \to a \times \to b = \to a \times \to c \Rightarrow \to b = \to c$