Let - PQR be a triangle- Let a-Q-R- b-R-P- If -a-12- -b-4-3 and b-c-24- then which of the following is are true-

The correct options are A |c⃗|^22 |a⃗|=12 B |a⃗×b⃗+c⃗×a⃗|=48√(3) D a⃗.b⃗= 72 Using vectors summation method, a⃗ = b⃗ + c⃗ |a⃗|^2 = |c ...

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Applications of Dot Product

Let Δ PQR b...

Question

Let $Δ P Q R$ be a triangle. Let $\to a = \to Q R, \to b = \to R P$ . If $| \to a | = 12, | \to b | = 4 \sqrt{3}$ and $\to b . \to c = 24$ , then which of the following is (are) true?

\frac{| \to c |^{2}}{2} - | \to a | = 12

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\frac{| \to c |^{2}}{2} + | \to a | = 30

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| \to a \times \to b + \to c \times \to a | = 48 \sqrt{3}

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\to a . \to b = - 72

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| \to a | = 1, ∣ ∣ \to b ∣ ∣ = \sqrt{2}

| \to c | = \sqrt{3}

\to a ⊥ (\to b + \to c)

\to b ⊥ (\to c + \to a)

\to c ⊥ (\to a + \to b)

∣ ∣ \to a + \to b + \to c ∣ ∣

[\to a \to b \to c] = 2

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

\to a, \to b, \to c

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

| \to a + \to b + \to c |^{2} =

\to a, \to b, \to c

\to a + \to b + \to c = 0

μ = \to a . \to b + \to b . \to c + \to c . \to a

| \to a | = 1; ∣ ∣ \to b ∣ ∣ = 4; | \to c | = 2

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

\to a, \to b

\to c

\to a . \to b \neq 0, \to b . \to c \neq 0

\to a

\to c

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