If a-b - -a x b- then - will be

Explanation for the correct option:Find the value of θ:Given, a·b = |a x b|⇒|a||b|cosθ = |a||b| sinθ [∵𝑎·𝑏=|a|| ...

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Standard XIII

Mathematics

General Solution of Trigonometric Equation

If a·b = |a x...

Question

If $a \cdot b = | a x b |$ , then $θ$ will be

$45 °$

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$60 °$

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$75 °$

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$30 °$

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Solution

The correct option is A
$45 °$

Explanation for the correct option:
Find the value of $θ$ :
Given, $a \cdot b = | a x b |$
$\Rightarrow$ $| a | | b | \cos θ = | a | | b | \sin θ$ $[∵ a \cdot b = | a | | b | c o s θ, | a \times b | = | a | | b | s i n θ]$
$\Rightarrow$ $\tan θ = 1$
$∴ θ = 45 °$
Hence, Option ‘A’ is Correct.

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If a·b=|axb|, then θ will be

The correct option is A 45°Explanation for the correct option:Find the value of θ:Given, a·b=|axb|⇒|a||b|cosθ=|a||b|sinθ ∵a·b=|a||b|cosθ,|a×b|=|a||b|sinθ⇒ tanθ=1∴θ=45°Hence, Option ‘A’ is Correct.

If $a \cdot b = | a x b |$ , then $θ$ will be