Multiple Choice
Given a vector with magnitude making an angle with the x-axis, what is the x component of ?
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2. 1D Motion / Kinematics
Vectors, Scalars, & Displacement
Multiple Choice
Can two vectors of unequal magnitude ever sum to ?
A
No, two vectors can only sum to if their magnitudes are both .
B
Yes, two vectors of any magnitude can always sum to if they are perpendicular.
C
Yes, two vectors of unequal magnitude can sum to if they are in the same direction.
D
No, two vectors can only sum to if they have equal magnitude and are in opposite directions.
Verified step by step guidance1
Recall that the sum of two vectors \( \vec{A} \) and \( \vec{B} \) is zero if and only if \( \vec{A} + \vec{B} = \vec{0} \). This means the two vectors must cancel each other out exactly.
For two vectors to cancel each other, they must have the same magnitude but point in exactly opposite directions. Mathematically, this means \( |\vec{A}| = |\vec{B}| \) and \( \vec{B} = -\vec{A} \).
If the magnitudes are unequal, no matter how you orient the vectors, their sum cannot be zero because the larger vector will always have a leftover component after adding the smaller one.
Vectors that are perpendicular cannot sum to zero unless both are zero vectors, because their directions are at 90 degrees and their sum will form a resultant vector with nonzero magnitude.
Therefore, the only way for two vectors to sum to zero is if they have equal magnitudes and are directed exactly opposite to each other.
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