If the foot of the perpendicular drawn from the origin to the plane is (4, −2, -5), then the equation of the plane is ______

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KollegeApply · Accepted Answer

4x − 2y − 5z = 45 Explanation: O ≡ (0, 0, 0) P ≡ (4, -2, -5) `vec"a"=4hat"i"-2hat"j"-5hat"k" vec"n"=vec"op"=4hat"i"-2hat"j"-5hat"k" ⇒ vec"PR".vec"n"=0 ⇒ [vec"r"-vec"a"].vec"n"=0 ⇒ vec"r".vec"n"-vec"a".vec"n"=0 ⇒ vec"r".(4hat"i"-2hat"j"-5hat"k")-(4hat"i"-2hat"j"-5hat"k").(4hat"i"-2hat"j"-5hat"k")=0 ⇒ vec"r".(4hat"i"-2hat"j"-5hat"k")-[16+4+25]=0 ⇒ vec"r"=xhat"i"+"y"hat"j"+"z"hat"k" R ≡ (x, y, z) ⇒ (xhat"i"+"y"hat"j"+"z"hat"k").(4hat"i"-2hat"j"-5hat"k")=45` ⇒ 4x - 2y - 5z = 45

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