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Dot Product of Two Vectors

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Question

Find $∣ ∣ ∣ \to a - \to b ∣ ∣ ∣$ , if two vectors $\to a$ and $\to b$ are such that $∣ ∣ \to a ∣ ∣ = 2, ∣ ∣ ∣ \to b ∣ ∣ ∣ = 3$ and $\to a . \to b = 4$

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Solution

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

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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

a

b

are the two vectors such that

| a | = 3 \sqrt{3}, | b | = 4

| a + b | = \sqrt{7}

, then the angle between

a

b

a

b

are two non-collinear vectors such that

| a | = 3, | b | = 4

a - b =^i + 2^j + 3^k

, then the value of

{\frac{| a - b |}{| a | | b |}}^{2}

Q. If a, b are two vectors such that

| a | = \sqrt{2}

| b | = 2

a . b = \sqrt{6}

. Find the angle between a and b.

\to a

\to b

are two vectors such that

| \to a | = 1, ∣ ∣ \to b ∣ ∣ = 4

\to a . \to b = 2

\to c = (2 \to a \times \to b) - 3 \to b

, then find the angle between

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