Let a- b- c- be three unit vectors and a-b-a-c-0- If the angle between b- and c- is -3 then - - a- b- c- - - is equal to

The correct option is A √(3)2 a.(b×c) Now a is perpendicular to b and c both.And b×c is also perpendicular to b and ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Limits

Let a⃗, b⃗,...

Question

Let $\to a, \to b, \to c$ be three unit vectors and $\to a . \to b = \to a . \to c = 0$ . If the angle between $\to b$ and $\to c$ is $\frac{π}{3}$ then $∣ ∣ [\begin{matrix} \to a & \to b & \to c \end{matrix}] ∣ ∣$ is equal to

\frac{\sqrt{3}}{2}

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\frac{1}{2}

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1

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Solution

The correct option is A $\frac{\sqrt{3}}{2}$
$\to a . (\to b \times \to c)$
Now $\to a$ is perpendicular to $\to b$ and $\to c$ both.
And $\to b \times \to c$ is also perpendicular to $\to b$ and $\to c$ both.
Hence $\to a$ is parallel to $\to b \times \to c$
Therefore
$| \to a . (\to b \times \to c) |$
$= a . | \to b \times \to c |$
$= 1 (b . c . cos \frac{π}{3})$

$= 1.1.1. \frac{\sqrt{3}}{2}$

$= \frac{\sqrt{3}}{2}$

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Let →a,→b,→c be three unit vectors and →a.→b=→a.→c=0. If the angle between →b and →c is π3 then ∣∣[→a→b→c]∣∣ is equal to

The correct option is A √32→a.(→b×→c)Now →a is perpendicular to →b and →c both.And →b×→c is also perpendicular to →b and →c both.Hence →a is parallel to →b×→cTherefore|→a.(→b×→c)|=a.|→b×→c|=1(b.c.cosπ3)=1.1.1.√32=√32

Let $\to a, \to b, \to c$ be three unit vectors and $\to a . \to b = \to a . \to c = 0$ . If the angle between $\to b$ and $\to c$ is $\frac{π}{3}$ then $∣ ∣ [\begin{matrix} \to a & \to b & \to c \end{matrix}] ∣ ∣$ is equal to