HSC Science (General) 12th Board ExamMaharashtra State Board
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If from a Point Q (A, B, C) Perpendiculars Qa and Qb Are Drawn to the Yz and Zx Planes Respectively, Then Find the Vector Equation of the Plane Qab. - HSC Science (General) 12th Board Exam - Mathematics and Statistics

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Question

If from a point Q (a, b, c) perpendiculars QA and QB are drawn to the YZ and ZX planes respectively, then find the vector equation of the plane QAB.

Solution

QA and QB are the perpendiculars drawn from the point Q(a,b,c)to YZ and ZX planes

`therefore A=(0, b,c) and B=(a,0,c)`

The required plane is pasing through O(0, 0, 0), A(0, b, c) and B(a, 0, c) 
The vector equation of the plane passing thorugh the O, A, B is

`bar r.(bar(OA)xxbar(OB))=bar 0.(bar(OA)xxbar(OB))`

let `bar r.(bar xxbar b)=0`

Now `bar(OA)=bara=0.hati+bhatj+chatk`

`bar(OB)=barb=ahati+0hatj+chatk`

`therefore bar(OA)xxbar(OB)=|[hati,hatj,hatk],[0,b,c],[a,0,c]|`

`=(bc-0)hati-(0-ac)hatj+(0-ab)hatk`

`=bchati+achatj-abhatk`

from (1), the vector equation of the required plane is

`barr.(bchati+achatj-abhatk)=0`

 

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APPEARS IN

 2016-2017 (March) (with solutions)
Question 1.2.3 | 2.00 marks
Solution If from a Point Q (A, B, C) Perpendiculars Qa and Qb Are Drawn to the Yz and Zx Planes Respectively, Then Find the Vector Equation of the Plane Qab. Concept: Trigonometric Functions - Trigonometric equations.
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