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help please eager to solve

help please eager to solve

Question Image
Grade:12

1 Answers

Yash Jain
55 Points
6 years ago
It is really very easy question Milind. See, we know all the points A,B,C,D. So we can easily find the equation of AB and CD using the symmetric form of line. AB is (x-6)/10 = (y+7)/-12 = z/-4 = m(say) and  CD is x/2 = (y-3)/-8 = (z+6)/16 = n(say). 1 proof can go like this:- just satisfy the given point on both the lines and hence...the result. Another one is bit lengthy but, is the appropriate approach. Get the gen. pt. on both the lines and equate them to get the point of intersection. The gen. pt. for AB is (10m+6,-12m-7,-4m) and that for CD is (2n,-8n+3,16n-6). So, on equating the resp abscissa, ordinate and applicate, we get m=-1/2 and n=1/2. Putting these values in the resp gen. pts. we get the same values for both i.e., (1,-1,2). Hence, the given point is the point of intersection of the lines AB and CD.

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