If a-b-c are three unit vectors such that a-b-a-c-0 and the angle between b and c is -3- then the value of -a-b-a-c- is

A·b=a·c=0 ⇒a⊥b and a⊥c ⇒a⊥(b c) |a×b a×c| =|a×(b c)| =|a||(b c)|sinπ2 =|b c| =√(|b|^2+|c|^2 2b·c) =√(1+1 1) =1 ...

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Standard XII

Mathematics

Applications of Cross Product

If a,b,c are ...

Question

If $\to a, \to b, \to c$ are three unit vectors such that $\to a \cdot \to b = \to a \cdot \to c = 0$ and the angle between $\to b$ and $\to c$ is $\frac{π}{3},$ then the value of $| \to a \times \to b - \to a \times \to c |$ is

\frac{1}{2}

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1

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2

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\frac{1}{3}

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Solution

The correct option is B $1$
$\to a \cdot \to b = \to a \cdot \to c = 0$
$\Rightarrow \to a ⊥ \to b$ and $\to a ⊥ \to c$
$\Rightarrow \to a ⊥ (\to b - \to c)$

$| \to a \times \to b - \to a \times \to c |$
$= | \to a \times (\to b - \to c) |$
$= | \to a | | (\to b - \to c) | sin \frac{π}{2}$
$= | \to b - \to c |$
$= \sqrt{| \to b |^{2} + | \to c |^{2} - 2 \to b \cdot \to c}$
$= \sqrt{1 + 1 - 1}$
$= 1$

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Applications of Cross Product

Standard XII Mathematics

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If →a,→b,→c are three unit vectors such that →a⋅→b=→a⋅→c=0 and the angle between →b and →c is π3, then the value of |→a×→b−→a×→c| is

The correct option is B 1→a⋅→b=→a⋅→c=0 ⇒→a⊥→b and →a⊥→c ⇒→a⊥(→b−→c) |→a×→b−→a×→c| =|→a×(→b−→c)| =|→a||(→b−→c)|sinπ2 =|→b−→c| =√|→b|2+|→c|2−2→b⋅→c =√1+1−1 =1

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