<prompt> Ikiwa mathbfa 3 na mathbfb 4, kisha tafuta k zote ambazo vekta mathbfa k mathbfb na mathbfa - k mathbfb ni orthogonal.  <response>: Wakati mathbfa k mathbfb na mathbfa - k mathbfb ni orthogonal, bidhaa zao za nukta ni 0:mathbfa k mathbfb cdot mathbfa - k mathbfb 0.Kupanua, tunapatamathbfa cdot mathbfa - k mathbfa cdot mathbfb k mathbfa cdot mathbfb - k2 mathbfb cdot mathbfb 0.Kwa kuwa mathbfa cdot mathbfa mathbfa2 9 na mathbfb cdot mathbfb mathbfb2 16, tumebakiwa na 9 - 16k2 0. Kisha k2 frac916, kwa hivyo thamani zinazowezekana za k ni frac34, -frac34. 