Suppose two initial vectors intersect at a right angle and form a resultant vector. The magnitudes of one initial vector, cap A , and the resultant vector, cap r , are given. Which formula can be used to find the magnitude of the other initial vector, cap b ?
Answer
A
cap b squared is equal to cap A plus cap r
B
cap b squared is equal to cap r squared minus cap A squared
C
cap b squared is equal to cap r squared plus cap A squared
D
cap b squared is equal to cap A squared minus cap r squared
Explanation
Because the initial vectors meet at a right angle, their magnitudes and the resultant form a right triangle. The resultant magnitude r is the hypotenuse, so the Pythagorean theorem gives r² = A² + b². Rearranging gives b² = r² − A², which is choice D.
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