If a-b- -0 and a-b- -0 then which one of the following is correct-

The correct option is C a⃗ =0 or b⃗ =0 #160; a . b =0 #160; ⇒ a =0 or b =0 #160;or a perpendicular b #160; ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a⃗·b⃗ =0...

Question

If $\to a \cdot \to b = 0$ and $\to a \times \to b = 0$ then which one of the following is correct?

\to a

is parallel to

\to b

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\to a

is perpendicular to

\to b

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\to a = 0

\to b = 0

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None of the above

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Solution

The correct option is C $\to a = 0$ or $\to b = 0$
$\to a . \to b = 0$
$\Rightarrow \to a = 0$ or $\to b = 0$ or $\to a$ perpendicular $\to b$
$\to a \times \to b = 0$
$\Rightarrow \to a = 0$ or $\to b = 0$ or $\to a$ parallel $\to b$
Thus, $\to a = 0$ or $\to b = 0$
Hence, option C is correct.

Suggest Corrections

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, then

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Nonzero vectors $\to a, \to b, \to c$ satisfy $\to a . \to b$ =0, $(\to b - \to a) . (\to b + \to c)$ = 0 and 2 $| \to b + \to c | = | \to b - \to a |$ .

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If →a⋅→b=0 and →a×→b=0 then which one of the following is correct?

The correct option is C →a=0 or →b=0 →a.→b=0 ⇒→a=0 or →b=0 or →a perpendicular →b →a×→b=0 ⇒→a=0 or →b=0 or →a parallel →b Thus, →a=0 or →b=0Hence, option C is correct.

If $\to a \cdot \to b = 0$ and $\to a \times \to b = 0$ then which one of the following is correct?

The correct option is C $\to a = 0$ or $\to b = 0$
$\to a . \to b = 0$
$\Rightarrow \to a = 0$ or $\to b = 0$ or $\to a$ perpendicular $\to b$
$\to a \times \to b = 0$
$\Rightarrow \to a = 0$ or $\to b = 0$ or $\to a$ parallel $\to b$
Thus, $\to a = 0$ or $\to b = 0$
Hence, option C is correct.