Let a- be a vector perpendicular to unit vectors b- and c- and if the angle between b- and c- is - then b-c- is

The correct option is A ±(sinα)a⃗ a⃗ b⃗=0 a⃗ c⃗=0 b⃗ c⃗=cosα b⃗×c⃗=ka⃗ #160; #160;( a⃗ is parallel to b⃗×c⃗) | b⃗ ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

Let a⃗ be a...

Question

Let $\to a$ be a vector perpendicular to unit vectors $\to b$ and $\to c$ and if the angle between $\to b$ and $\to c$ is $α$ , then $\to b \times \to c$ is

\pm (cos α) \to a

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\pm (cosec α) \to a

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\pm (sin α) \to a

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\pm tan α

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Solution

The correct option is A $\pm (sin α) \to a$
$\to a - \to b = 0$
$\to a - \to c = 0$
$\to b - \to c = cos α$
$\to b \times \to c = k \to a$ ( $\to a$ is parallel to $\to b \times \to c)$
$∣ ∣ \to b \times \to c ∣ ∣ = | k \to a |$
$| k | = sin α$
$\to b \times \to c = \pm (sin α) \to a$

Suggest Corrections

Similar questions

Q. Let

\to a, \to b, \to c

be three units vectors such that

\to a \times (\to b \times \to c) = \frac{\to b + \to c}{\sqrt{2}}

and the angles between

\to a, \to c

and

\to a, \to b

α

and

β

respectively, then

Q. Let

\to a, \to b

and

\to c

be three unit vectors such that

\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b \times \to c) \cdot

\to b

is not parallel to

\to c .

Then the angle between

\to a

and

\to b

Q. Let

\to a, \to b

and

\to c

be three vectors such that

| \to a | = \sqrt{3}, | \to b | = 5, \to b . \to c = 10

and the angle between

\to b

and

\to c

\frac{π}{3} .

\to a

is perpendicular to vector

\to b \times \to c

, then

| \to a \times (\to b \times \to c) |

is equal to

Q. Let

\to a, \to b

and

\to c

be three unit vector such that

\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)

. If

\to b

is not parallel to

\to c

. then angle between

\to a

and

\to b

is:

Q. If

\to a, \to b, \to c

are unit vectors such that

\to a

is perpendicular to the

\to b

and

\to c

and angle between

\to b

and

\to c

\frac{π}{3}

, then value of

| \to a +

\to b +

\to c |

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Let →a be a vector perpendicular to unit vectors →b and →c and if the angle between →b and →c is α, then →b×→c is

The correct option is A ±(sinα)→a→a−→b=0→a−→c=0→b−→c=cosα→b×→c=k→a (→a is parallel to →b×→c)∣∣→b×→c∣∣=|k→a||k|=sinα→b×→c=±(sinα)→a

Let $\to a$ be a vector perpendicular to unit vectors $\to b$ and $\to c$ and if the angle between $\to b$ and $\to c$ is $α$ , then $\to b \times \to c$ is

The correct option is A $\pm (sin α) \to a$
$\to a - \to b = 0$
$\to a - \to c = 0$
$\to b - \to c = cos α$
$\to b \times \to c = k \to a$ ( $\to a$ is parallel to $\to b \times \to c)$
$∣ ∣ \to b \times \to c ∣ ∣ = | k \to a |$
$| k | = sin α$
$\to b \times \to c = \pm (sin α) \to a$