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Question 11 of 36

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SAT Subject Test

When a vector of magnitude 6 units is added to a vector of magnitude 8 units, the magnitude of the resultant vector will be

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exactly 2 units

Correct Answer: 
No

exactly 10 units

Correct Answer: 
No

exactly 14 units

Correct Answer: 
No

0 units, 10 units, or some value between them

Correct Answer: 
No

2 units, 14 units, or some value between them

Correct Answer: 
Yes

The correct answer is 2 units, 14 units, or some value between them. When two vectors are added, the magnitude of the resultant vector depends on the angle between them. The greatest value a resultant vector can have is when both vectors point in the same direction. In this case the angle is zero and the magnitudes of the two vectors can be directly added, 6 units + 8 units = 14 units. The least value a resultant vector can have is when the vectors point directly opposite to each other so the angle is 180 degrees. The magnitude of the smaller vector is then subtracted from that of the larger one, 8 units - 6 units = 2 units. For any other angle the magnitude of the resultant vector is between 2 units and 14 units.

Question Difficulty: 
easy