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AP EAMCET201921 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

If A=(1,8,4), B=(2,-3,1) , then the direction cosines of a normal to the plane A O B is

Options

  1. A2 78 , 5 78 , -7 78
  2. B2 10 9 , 7 10 90 , -19 10 90
  3. C4 218 , 9 218 , -11 218
  4. D2 11 , 6 11 , -9 11

Correct answer

B. 2 10 9 , 7 10 90 , -19 10 90

Step-by-step solution

Given, A=(1,8,4) and B=(2,-3,1) aligned & O A = i +8 j +4 k & and O B =2 i -3 j + k & Now, n = O A O B | O A O B | & aligned Here, O A O B = | array ccc i & j & k 1 & 8 & 4 2 & -3 & 1 array | aligned & = i (8+12)- j (1-8)+ k (-3-16)=20 i +7 j -19 k & and | O A O B |= (20)^2+7^2+(-19)^2 & = 400+49+361 = 810 =9 10 & n = 2 0 i +7 j -19 k 9 10 & aligned Direction cosines are 20 9 10 , 7 9 10 , -19 9 10 i.e. 2 10 9 , 7 10 90 , -19 10 90

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