Answer to Question #349439 in Analytic Geometry for eyay

Question #349439

Determine the value of 𝑎 so that 𝑨 = 2𝒊 − 𝑎𝒋 + 𝒌 and 𝑩 = 4𝒊 − 2𝒋 − 2𝒌 are perpendicular.


1
Expert's answer
2022-06-10T09:03:31-0400

"A=(2,-a,1)", "B=(4,-2,-2)".


Two vectors are perpendicular iff "A\\cdot B=0".


"A\\cdot B=2\\cdot4 + (-a)\\cdot(-2) + 1\\cdot(-2)=8+4a-2=4a+6".


"4a+6=0", so "a=-\\frac32".


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