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negation
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Homework Statement
The sum of two vectors, A→ + B→, is perpendicular to their difference, A→ - B→. How do the vectors magnitude compare?
The Attempt at a Solution
SQRT[(A+B)^2 + (A-B)^2]
voko said:Have you studied the scalar (dot) product of vectors?
BvU said:What does perpendicularity mean for the dot product ? write it out as a vector expression, then use the distributive property of the dot product.
voko said:Have you studied the scalar (dot) product of vectors?
BvU said:What does perpendicularity mean for the dot product ? write it out as a vector expression, then use the distributive property of the dot product.
voko said:See, it was not that hard :)
voko said:I do not understand how your assumption is related to the problem.
The sum of vectors is a mathematical operation that combines two or more vectors into a single vector. This operation is also known as vector addition.
To calculate the sum of vectors, you need to add the corresponding components of each vector. For example, if you have two vectors, v1 = (x1, y1) and v2 = (x2, y2), the sum of these vectors would be (x1+x2, y1+y2).
If two vectors are in the same direction, their sum will result in a vector with a larger magnitude, pointing in the same direction as the original vectors.
If two vectors are in opposite directions, their sum will result in a vector with a smaller magnitude, pointing in the direction of the larger vector.
Yes, the sum of vectors can be negative. This can happen when the vectors are in opposite directions and have different magnitudes, resulting in a vector with a negative magnitude.