Equation of plane passing through points given by position vectors $¯ a a n d ¯ b$ and origin will be

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Solution

The correct option is C

Here we know given the plane passes through points given by position vectors $¯ a a n d ¯ b$ . So the perpendicular to the plane will be along $¯ a \times ¯ b$ . Therefore our $^n$ or unit vector perpendicular to the plane will be $\frac{¯ a \times ¯ b}{| ¯ a \times ¯ b |}$ . Equation of plane will be

$(¯ r - 0) . \frac{¯ a \times ¯ b}{| ¯ a \times ¯ b |} = 0.$

Which is same as,

$¯ r . \frac{¯ a \times ¯ b}{| ¯ a \times ¯ b |} = 0.$

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Equation of plane passing through points given by position vectors ¯a and ¯b and origin will be

Equation of plane passing through points given by position vectors $¯ a a n d ¯ b$ and origin will be