For any two vectors a- -b- prove that - a-b- 2 -a- -a- a- -b- b- -a- b-b-

L.H.S:|a⃗×b⃗|^2=|a⃗|^2|b⃗|^2 sin ^2 θ R.H.S:(a⃗.a⃗)(b⃗.b⃗) (a⃗.b⃗)(b⃗.a⃗) =|a⃗|^2|b⃗|^2 (a⃗.b⃗)^2(∵a⃗.b⃗=b⃗.a⃗) =|a⃗|^2|b⃗|^2 (|a⃗||b⃗|cosθ) ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Applications of Cross Product

For any two v...

Question

For any two vectors $\to a, \to b$ , prove that ${∣ ∣ \to a \times \to b ∣ ∣}^{2} = ∣ ∣ ∣ \begin{matrix} \to a . \to a & \to a . \to b \to b . \to a & \to b . \to b \end{matrix} ∣ ∣ ∣$

Open in App

Solution

Suggest Corrections

Similar questions

^a

^b

| \to a + \to b | \leq | \to a | + | \to b |

| \to a - \to b | \leq | \to a | + | \to b |

| \to a | \to b + | \to b | \to a

| \to a | \to b - | \to b | \to a

\to a

\to b

| \to a | \to b + | \to b | \to a

| \to a | \to b - | \to b | \to a

\to a

\to b

\to a

\to b

| \to a \times \to b |^{2} = | \to a |^{2} | \to b |^{2} - | \to a . \to b |^{2}

\to a, \to b

\to c

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

\to a + \to b, \to b + \to c, \to c + \to a

\to a, \to b, \to c

Join BYJU'S Learning Program