Find -a- and -b- if a-b-a-b-8 and -a-8-b-

(a⃗+b⃗)(a⃗ b⃗)=8—(1) | a⃗ |=8 | b⃗ | Form (1) | a⃗ |^2 | b⃗ |^2=8 | a⃗ |^2 | b⃗ |^2=8 #160; ⇒ 64 | b⃗ |^2 | b⃗ |^2=8 | b |^2 ...

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Applications of Cross Product

Find |a⃗| a...

Question

Find $| \to a |$ and $| \to b |$ , if $(\to a + \to b) . (\to a - \to b) = 8$ and $| \to a | = 8 | \to b |$ .

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Solution

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| \to b |

(\to a + \to b) \cdot (\to a - \to b) = 8

| \to a | = 8 | \to b |

\to a

\to b

| \to a | = 4, ∣ ∣ \to b ∣ ∣ = 3

\to a \to b = 8

∣ ∣ \to a \times \to b ∣ ∣

| \to a | = 2, | \to b = 5 |

| \to a \times | \to b | = 8

\to a, \to b

| \to a | = 8, | \to b | = 3

| \to a \times \to b | = 12

\to a

\to b

\to a = 3^i + 4^j

\to b = 2^i - 3^j

(\to a + \to b) . (\to a - \to b)

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