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MATH / If ‖a‖=3 and ‖b‖=4, then find all k for which the vectors a+kb and a−kb are orthogonal.

Problem

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problem

If ‖a‖=3\|\mathbf{a}\| = 3 and ‖b‖=4,\|\mathbf{b}\| = 4, then find all kk for which the vectors a+kb\mathbf{a} + k \mathbf{b} and a−kb\mathbf{a} - k \mathbf{b} are orthogonal.
Plain-text mathematical notation (without MathML)
If ‖a‖=3 and ‖b‖=4, then find all k for which the vectors a+kb and a−kb are orthogonal.
Original LaTeX notation
If $\|\mathbf{a}\| = 3$ and $\|\mathbf{b}\| = 4,$ then find all $k$ for which the vectors $\mathbf{a} + k \mathbf{b}$ and $\mathbf{a} - k \mathbf{b}$ are orthogonal.

level

Level 3

type

Precalculus

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Source and history

task_id
e0528f97-5118-56d8-a3bf-0c58f5d89760
task_key
precalculus--test--e0528f97-5118-56d8-a3bf-0c58f5d89760
task_revision_id
1
config / split
precalculus / test

Official source

initial import