If a- and b- are any two vectors- then the value of -a-b-2- -a-b-2 equals

The correct option is D a^2b^2 |a·b|^2 + |a×b|^2 = (ab cosθ )^2+(ab sinθ )^2 #160; #160; #160; #160; #160; #160; #160; #160; ...

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Standard XII

Mathematics

Definition of Vector

if a⃗ and ...

Question

if $\to a$ and $\to b$ are any two vectors, then the value of $| \to a \cdot \to b |^{2}$ + $| \to a \times \to b |^{2}$ equals

a^{2} b^{2}

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2 a^{2} b^{2}

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Solution

The correct option is D $a^{2} b^{2}$
$| \to a \cdot \to b |^{2} + | \to a \times \to b |^{2} = (a b cos θ)^{2} + (a b sin θ)^{2}$
$= a^{2} b^{2} ({cos}^{2} θ + {sin}^{2} θ)$
$= a^{2} b^{2}$

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if →a and →b are any two vectors, then the value of |→a⋅→b|2+|→a×→b|2 equals

The correct option is D a2b2|→a⋅→b|2+|→a×→b|2=(abcosθ)2+(absinθ)2 =a2b2(cos2θ+sin2θ) =a2b2

if $\to a$ and $\to b$ are any two vectors, then the value of $| \to a \cdot \to b |^{2}$ + $| \to a \times \to b |^{2}$ equals

The correct option is D $a^{2} b^{2}$
$| \to a \cdot \to b |^{2} + | \to a \times \to b |^{2} = (a b cos θ)^{2} + (a b sin θ)^{2}$
$= a^{2} b^{2} ({cos}^{2} θ + {sin}^{2} θ)$
$= a^{2} b^{2}$