Consider three vectors ^p=^i+^j,^q=2^i+4^j−^k,^r=^i+3^k. if ^p,^q,^r denotes the position vector of three non collinear points then the equation of the plane containing these points is
A
8x−3y−z−5=0
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B
x−3y+2z=0
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C
3x−y+z=0
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D
3x−y−2=0
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Solution
The correct option is A8x−3y−z−5=0 Equation of plane passing through →p=^i+^j is given by, a(x−1)+b(y−1)+cz=0 Given plane containing →q=2^i+4^j−1^k ⇒a+3b−c=0......(1) It also has →r=^i+3^k ⇒−b+3c=0.....(2) Solving (1) and (2), we get a=−8c,b=3c Hence, required plane is