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Let DeltaPQR be a triangle. Let vec(a) =...

Let `DeltaPQR` be a triangle. Let `vec(a) = vec(QR), vec(b) = vec(RP) and vec(c) = vec(PQ)`. If `|vec(a)| = 12, |vec(b)| = 4 sqrt3 and vec(b).vec(c) = 24`, then which of the following is (are) true?

A

`(|vec(c)|^(2))/(2) - |vec(a)| = 12`

B

`(|vec(c)|^(2))/(2) + |vec(a)| = 30`

C

`|vec(a) xx vec(b) + vec(c) xx vec(a)|= 48 sqrt3`

D

`vec(a).vec(b) = -72`

Text Solution

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The correct Answer is:
A, C, D
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