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Common Core: High School - Number and Quantity : Magnitude and Direction of a Vector Sum: CCSS.Math.Content.HSN-VM.B.4b

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Example Questions

Example Question #51 : Vector & Matrix Quantities

If $\left \| v\right \|=9$ , and $\left \| w\right \|=28$ , and the angle in between them is $150^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=33.98$

$\left \| v+w\right \|=29.53$

$\left \| v+w\right \|=36.89$

$\left \| v+w\right \|=35.76$

$\left \| v+w\right \|=36.08$

Correct answer:

$\left \| v+w\right \|=36.08$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=9 , b=28 , and $C=150^{\circ}$ , then

$c^2=9^2+28^2-2\cdot9\cdot28\cos(150^{\circ})$

$c^2=81+784-18\cdot28\cos(150^{\circ})$

$c^2=865-504\cos(150^{\circ})$

$c^2=865-504\cdot-0.8660254$

c^2=865+436.4768

c^2=1301.477

$\sqrt{c^2}=\sqrt{1301.477}$

$c=\sqrt{1301.477}\approx36.08$

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Example Question #52 : Vector & Matrix Quantities

If $\left \| v\right \|=12$ , and $\left \| w\right \|=34$ , and the angle in between them is $54^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=24.87$

$\left \| v+w\right \|=29.67$

$\left \| v+w\right \|=26.67$

$\left \| v+w\right \|=28.64$

$\left \| v+w\right \|=28.14$

Correct answer:

$\left \| v+w\right \|=28.64$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=12 , b=34 , and $C=54^{\circ}$ , then

$c^2=12^2+34^2-2\cdot12\cdot34\cos(54^{\circ})$

$c^2=144+1156-24\cdot34\cos(54^{\circ})$

$c^2=1300-816\cos(54^{\circ})$

$c^2=1300-816\cdot0.5877853$

c^2=1300-479.6328

c^2=820.3672

$\sqrt{c^2}=\sqrt{820.3672}$

$c=\sqrt{820.3672}\approx28.64$

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Common Core: High School - Number and Quantity : Magnitude and Direction of a Vector Sum: CCSS.Math.Content.HSN-VM.B.4b

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #51 : Vector & Matrix Quantities

Example Question #52 : Vector & Matrix Quantities

All Common Core: High School - Number and Quantity Resources

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