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

The correct option is B 1 a⃗, b⃗, c⃗ are unit vectors such that a⃗·b⃗ = 0 #160; = a⃗·c⃗ and the angle between b⃗ and c⃗ is ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

If a⃗, b⃗, ...

Question

If $\to a, \to b, \to c$ are unit vectors such that $\to a \cdot \to b = 0 = \to a \cdot \to c$ 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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Solution

The correct option is B $1$
$\to a, \to b, \to c$ are unit vectors such that $\to a \cdot \to b = 0 = \to a \cdot \to c$ and the angle between $\to b$ and $\to c$ is $\frac{π}{3}$
$\to a \cdot (\to b - \to c) = 0$
i.e angle between $\to a$ and $\to b - \to c$ is $\frac{π}{2}$
$∴ | \to a \times \to b - \to a \times \to c | = | \to a \times (\to b - \to c) |$
$\Rightarrow | \to a | | \to b - \to c | = \sqrt{{\to b}^{2} + {\to c}^{2} - 2 \to b \cdot \to c}$
$\Rightarrow | \to a | | \to b - \to c | = \sqrt{1 + 1 - 2 (\frac{1}{2})}$
$∴ | \to a \times \to b - \to a \times \to c | = 1$

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

If $\to a, \to b, \to c$ are unit vectors such that $\to a \cdot \to b = 0 = \to a \cdot \to c$ 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