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

ConceptTrigonometric Functions Trigonometric equations

#### 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

Is there an error in this question or solution?

#### 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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