The lines x-1/2=y+1/2=z-1/1 and x-3/1=y-k/2=z/1 intersect each other at point

Correct Answer is : (-2, -4 ,-5 )

Correct Answer is : (-2, -4 ,-5 )

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MHT CET 2017 Math Solved Paper

Question : 49 of 50

Marks: +1, -0

The lines

\frac{x-1}{2}=\frac{y+1}{2}=\frac{z-1}{1}

\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}

intersect each other at point

Solution:

(b) Since,

\frac{x-1}{2}=\frac{y+1}{2}=\frac{z-1}{1}

= λ ......(i)

and ,

\frac{x-3}{1}=\frac{y-6}{2}=\frac{z}{1}

......(ii)

Now, any point on the line (i) is P(2 λ + 1 , 2λ-1, 4λ+1)

∴

\frac{2\lambda + 1-3}{1}=\frac{2\lambda -1-6}{2}=\frac{4\lambda + 1}{1}

[from (ii)]

So, 4 λ - 4 = 2λ - 7 ⇒ 2λ = -3

Hence, point of intersection P is

= (2 \times \left(-\frac{3}{2}\right)+1

2 \times \left(-\frac{3}{2}\right)-1

4 \times \left(-\frac{3}{2}\right)+1 )

≡

(-2,-4,-5)

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