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Work Done as Dot Product

If | a |=4,...

Question

If $∣ ∣ \to a ∣ ∣ = 4$ , $∣ ∣ ∣ \to b ∣ ∣ ∣ = 2$ and the angle between $\to a$ and $\to b$ is $\frac{π}{6}$ , then $(\to a \times \to b)$ is equal to

A

48

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B

4

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C

{∣ ∣ ∣ \to b ∣ ∣ ∣}^{2}

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D

None of these

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Solution

The correct options are
B $4$
C ${∣ ∣ ∣ \to b ∣ ∣ ∣}^{2}$
$∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣$
$= ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ sin θ$
$= 4 \times 2 \times sin \frac{π}{6} = 4$

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Similar questions

¯ ¯ c

is perpendicular to

¯ ¯ ¯ a

¯ ¯ b

∣ ∣ ¯ ¯ ¯ a ∣ ∣ = 3, ∣ ∣ ¯ ¯ b ∣ ∣ = 4, ∣ ∣ ¯ ¯ c ∣ ∣ = 5

and the angle between

¯ ¯ ¯ a

¯ ¯ b

\frac{π}{6}

[¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] =

| \to a | = 4, | \to b | = 2

and the angle between

\to a

\to b

\frac{π}{6}

| \to a \times \to b |^{2}

¯ ¯ ¯ a

is perpendicular to both

¯ ¯ b

¯ ¯ c

. The angle between

¯ ¯ b

¯ ¯ c

\frac{2 π}{3}

∣ ∣ ¯ ¯ ¯ a ∣ ∣ = 2, ∣ ∣ ¯ ¯ b ∣ ∣ = 3, ∣ ∣ ¯ ¯ c ∣ ∣ = 4

¯ ¯ c . (¯ ¯ ¯ a \times ¯ ¯ b) =

| a \times b | = 4 a n d | a . b | = 2, t h e n {| a |}^{2} {| b |}^{2}

\to a

is perpendicular to

\to b

\to c,

∣ ∣ \to a ∣ ∣ = 2, ∣ ∣ ∣ \to b ∣ ∣ ∣ = 3, ∣ ∣ \to c ∣ ∣ = 4

and the angle between

\to b

\to c

\frac{2 π}{3}

[\to a \to b \to c]

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