A ⋅ B = 0 means thatGroup of answer choicesA and B are perpendicularA and B are colinearA and B are parallelNone of the above
Question
A ⋅ B = 0 means thatGroup of answer choicesA and B are perpendicularA and B are colinearA and B are parallelNone of the above
Solution
A ⋅ B = 0 means that A and B are perpendicular.
Here's why:
The dot product (also known as the scalar product or inner product) in a Euclidean vector space is a way to multiply vectors together, with the result of this operation being a scalar.
The dot product of two vectors A and B is defined as:
A ⋅ B = ||A|| ||B|| cos(θ)
where: ||A|| is the magnitude (length) of vector A, ||B|| is the magnitude (length) of vector B, and θ is the angle between A and B.
When A ⋅ B = 0, this means that cos(θ) = 0, because the magnitudes of vectors (||A|| and ||B||) can't be zero (unless the vectors are zero vectors).
The cosine of an angle is zero only for θ = 90° (or π/2 in radians).
Therefore, if the dot product of two vectors is zero, this means that the angle between the vectors is 90 degrees, i.e., the vectors are perpendicular to each other.
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