If $\to a = ⟨ 7, - 2, 1 ⟩$ $veca = << 7,-2,1 >>$ and $\to b = ⟨ - 2, 6, 7 ⟩$ $vecb = << -2,6,7 >>$ , what is $\to a \cdot \to b - ∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ \cdot ∣ ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ ∣$ $vecacdotvecb - ||veca||cdot||vecb||$ ?

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If $\to a = ⟨ 7, - 2, 1 ⟩$ $veca = << 7,-2,1 >>$ and $\to b = ⟨ - 2, 6, 7 ⟩$ $vecb = << -2,6,7 >>$ , what is $\to a \cdot \to b - ∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ \cdot ∣ ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ ∣$ $vecacdotvecb - ||veca||cdot||vecb||$ ?

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Answer 1 · 2016-10-16T13:32:27

$- 19 - \sqrt{54 \cdot 89}$ $-19-sqrt(54*89)$

Explanation:

$\to a = (7, - 2, 1)$ $veca=(7,-2,1)$
$\to b = (- 2, 6, 7)$ $vecb=(-2,6,7)$
Dot product is
$\to a . \to b = 7 \cdot - 2 - 2 \cdot 6 + 7 \cdot 1 = - 14 - 12 + 7 = - 19$ $veca.vecb=7*-2-2*6+7*1=-14-12+7=-19$
$∣ ∣ ∣ ∣ \to a ∣ ∣ = \sqrt{7^{2} + 2^{2} + 1} = \sqrt{54}$ $∣∣veca∣∣=sqrt(7^2+2^2+1)=sqrt54$
$∣ ∣ ∣ ∣ \to b ∣ ∣ = \sqrt{2^{2} + 6^{2} + 7^{2}} = \sqrt{89}$ $∣∣vecb∣∣=sqrt(2^2+6^2+7^2)=sqrt89$
So the answer is
$\to a . \to b - ∣ ∣ \to a ∣ ∣ . ∣ ∣ \to b ∣ ∣ = - 19 - \sqrt{54 \cdot 89}$ $veca.vecb-∣∣veca∣∣.∣∣vecb∣∣=-19-sqrt(54*89)$

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If $\to a = ⟨ 7, - 2, 1 ⟩$ $veca = << 7,-2,1 >>$ and $\to b = ⟨ - 2, 6, 7 ⟩$ $vecb = << -2,6,7 >>$ , what is $\to a \cdot \to b - ∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ \cdot ∣ ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ ∣$ $vecacdotvecb - ||veca||cdot||vecb||$ ?

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Explanation:

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If →a=⟨7,−2,1⟩veca = << 7,-2,1 >> and →b=⟨−2,6,7⟩vecb = << -2,6,7 >>, what is →a⋅→b−∣∣∣∣→a∣∣∣∣⋅∣∣∣∣∣∣→b∣∣∣∣∣∣vecacdotvecb - ||veca||cdot||vecb||?

1 Answer

Explanation:

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If $\to a = ⟨ 7, - 2, 1 ⟩$ $veca = << 7,-2,1 >>$ and $\to b = ⟨ - 2, 6, 7 ⟩$ $vecb = << -2,6,7 >>$ , what is $\to a \cdot \to b - ∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ \cdot ∣ ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ ∣$ $vecacdotvecb - ||veca||cdot||vecb||$ ?