Vector B has x, y, and x components of 5.5, 7.1, and 1.4 units, respectively. How do you calculate the magnitude of vector B?

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Vector B has x, y, and x components of 5.5, 7.1, and 1.4 units, respectively. How do you calculate the magnitude of vector B?

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Answer 1 · 2016-07-14T16:59:32

$\sqrt{82.62} ≅ 9.09$ $sqrt82.62~=9.09$

Explanation:

If vector B, denoted by $\to B = (b_{1}, b_{2}, b_{3})$ $vecB=(b_1,b_2,b_3)$ , then its manitude,

denoted by $∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣$ $||vecB||$ , is defined by,

$∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣ = \sqrt{b_{1}^{2} + b_{2}^{2} + b_{3}^{2}}$ $||vecB||=sqrt(b_1^2+b_2^2+b_3^2)$

In our case, $∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣ = \sqrt{{5.5}^{2} + {7.1}^{2} + {1.4}^{2}} = \sqrt{30.25 + 50.41 + 1.96} = \sqrt{82.62} ≅ 9.09$ $||vecB||=sqrt{5.5^2+7.1^2+1.4^2}=sqrt(30.25+50.41+1.96)=sqrt82.62~=9.09$

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Vector B has x, y, and x components of 5.5, 7.1, and 1.4 units, respectively. How do you calculate the magnitude of vector B?

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