If | → a | = 4 , ∣ ∣ → B ∣ ∣ = 3 and → a . → B = 6 √ 3 , Then Find the Value of ∣ ∣ → a × → B ∣ ∣ . - Mathematics

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Sum

If `|vec"a"| = 4, |vec"b"| = 3` and `vec"a".vec"b" = 6 sqrt(3)`, then find the value of `|vec"a" xx vec"b"|`.

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Solution

As `vec"a".vec"b" = |vec"a"||vec"b"| cos theta = 6sqrt(3)`

⇒ `4 xx 3 xx cos theta = 6sqrt(3)`

⇒ `cos theta = sqrt(3)/(2)`

sin θ = `(1)/(2).`

Now,

`|vec"a" xx vec"b"| = |vec"a"||vec"b"| sin theta = 4 xx 3 xx (1)/(2) = 6`.

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