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Homework Statement
Show that
||b||a + ||a||b and ||b||a - ||a||b are orthogonal vectors.
Homework Equations
The Attempt at a Solution
After analyzing it and trying to prove it to no avail, I don't even think it's a true statement.
If two vectors are othogonal, their dot product will be zero. What do you get if you dot the two vectors in this problem?Homework Statement
Show that
||b||a + ||a||b and ||b||a - ||a||b are orthogonal vectors.
Homework Equations
The Attempt at a Solution
After analyzing it and trying to prove it to no avail, I don't even think it's a true statement.
True. If you form a parallelogram with a and b as two adjacent sides, then a + b will be a diagonal, and a - b will be the other diagonal. Most of the time these diagonals won't be perpendicular, so the dot product (a + b)##\cdot##(a - b) won't be zero.I mean the scalar multiplied by vector multiplication. The dot product is not always 0 for (a+b) * (a-b).
That's because you're essentially working with unit vectors, and the parallelogram is actually a square. In that case, the diagonals are perpendicular.I find it hard to grasp that the magnitudes are what made them orthogonal.