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TS EAMCET 11-Sep-2020 Shift 2 Solved Paper

Section: Mathematics

Question : 61 of 160

Marks: +1, -0

\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}

ax+by+z=7,

a+b=

Solution:

Given that, line

\;\frac{x-4}{1}=\;\frac{y-2}{1}=\;\frac{z-7}{2}

Line is passing through point

P(4,+2,7)

and direction ratios

(1,1,2)

and lies on the given plane

a x+b y+z=7

So, point will satisfy the equation of plane

a(4)+b(+2)+(7)=7

4 a+2 b=0

.....(i)

Now direction ratios of the line and direction ratios of the plane will be perpendicular so their product must be zero

a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}=(1)(a)+(1)(b)+(2)(1)

0=a+b+2

\;\; a+b=-2

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