A plane passes through the point ( 3 , 5 , 7 ) . If the direction ratios of its normal are equal to the intercepts made by the plane x + 3 y + 2 z = 9 with the coordinate axes, then the equation of that plane is

Step-by-step solution

Given: x + 3 y + 2 z = 9 ⇒ x 9 + y 3 + z 9 2 = 1 Comparing with the standard form x a + y b + z c = 1 , we get a = 9 → x - intercept b = 3 → y - intercept c = 9 2 → z - intercept So, the normal vector for the required plane is n → = 9 i ^ + 3 j ^ + 9 2 k ^ a → = 3 i ^ + 5 j ^ + 7 k ^ Equation of required plane, ⇒ r → · n → = a → · n → ⇒ r → · 9 i ^ + 3 j ^ + 9 2 k ^ = 3 i ^ + 5 j ^ + 7 k ^ · 9 i ^ + 3 j ^ + 9 2 k ^ &#8