This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Ili vekta mbili ziwe orthogonal (zimepangwa kwa pembe ya 90 digrii), dot product yao lazima iwe sifuri. Step 1: Andika vekta zilizotolewa. Tunapewa vekta: a = 2i + 3j b = xi + yj Step 2: Tumia masharti ya vekta za orthogonal. Vekta a na b ni orthogonal ikiwa dot product yao ni sifuri: a · b = 0 Step 3: Kokotoa dot product ya a na b. Dot product inakokotolewa kwa kuzidisha vijenzi vinavyolingana na kisha kujumlisha matokeo: a · b = (2)(x) + (3)(y) a · b = 2x + 3y Step 4: Weka dot product sawa na sifuri. Kwa kuwa vekta ni orthogonal, tunapata mlinganyo: 2x + 3y = 0 Step 5: Tafuta uhusiano kati ya x na y. Kutoka kwenye mlinganyo 2x + 3y = 0, tunaweza kueleza x kwa kutumia y au y kwa kutumia x. 2x = -3y x = -(3)/(2)y Au 3y = -2x y = -(2)/(3)x Kuna jozi nyingi zisizo na kikomo za (x, y) zinazokidhi masharti haya. Kwa mfano, ikiwa y=2, basi x = -(3)/(2)(2) = -3. Hivyo, b = -3i + 2j ingekuwa orthogonal kwa a. Thamani za x na y lazima zikidhi uhusiano: 2x + 3y = 0 Tuma swali linalofuata 📸