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Addition of Rational Expressions

| a | =2;| b ...

Question

$∣ ∣ \to a ∣ ∣ = 2; ∣ ∣ ∣ \to b ∣ ∣ ∣ = 3$ and $\to a . \to b = 4$ . Find $∣ ∣ ∣ \to a - \to b ∣ ∣ ∣$

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Solution

$| \to a | = 2$
$| \to b | = 3$
$| \to a . \to b | = 4$
$| \to a - \to b |^{2} = | a |^{2} + | b |^{2} - 2 a b$
$= 4 + 9 - 2 (4)$
$= 13 - 8 = 5$
$| \to a - \to b | = \sqrt{5}$

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Similar questions

| \to a - \to b |

, if two vectors

\to a

\to b

| \to a | = 2

| \to b | = 3

\to a . \to b = 4

I

| ¯ ¯ ¯ a . ¯ ¯ b | = | ¯ ¯ ¯ a \times ¯ ¯ b |

(¯ ¯ ¯ a . ¯ ¯ b) = \frac{π}{4}

II

| ¯ ¯ ¯ a . ¯ ¯ b |^{2} = | ¯ ¯ ¯ a \times ¯ ¯ b |^{2}

(¯ ¯ ¯ a, ¯ ¯ b) = \frac{3 π}{4}

∣ ∣ ¯ ¯ ¯ a \times ¯ ¯ b ∣ ∣

∣ ∣ ¯ ¯ ¯ a ∣ ∣ = 4

∣ ∣ ¯ ¯ b ∣ ∣ = 5

(¯ ¯ ¯ a . ¯ ¯ b) = - 6

.

| a | = 3, | ¯ ¯ b | = 4

¯ ¯ ¯ a . ¯ ¯ b = 8

| ¯ ¯ ¯ a \times ¯ ¯ b | =

∣ ∣ ¯ ¯ ¯ a ∣ ∣ = 2, ∣ ∣ ¯ ¯ b ∣ ∣ = 5

∣ ∣ ¯ ¯ ¯ a \times ¯ ¯ b ∣ ∣ = 8

¯ ¯ ¯ a . ¯ ¯ b

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