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Addition of Vectors

If |a⃗|=10,|b...

Question

If $| \to a | = 10, ∣ ∣ \to b ∣ ∣ = 2 a n d \to a . \to b = 12$ , then the value of $∣ ∣ \to a \times \to b ∣ ∣ =$

A

5

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B

10

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C

14

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D

16

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Solution

The correct option is D
16

${(¯ a . \to b)}^{2} + ∣ ∣ ¯ a \times \to b ∣ ∣ = {| ¯ a |}^{2} {∣ ∣ \to b ∣ ∣}^{2} \Rightarrow 144 + ∣ ∣ ¯ a \times \to b ∣ ∣ = 100 \times 4 {∣ ∣ ¯ a \times \to b ∣ ∣}^{2} = 256 ∣ ∣ ¯ a \times \to b ∣ ∣ = 16$

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