Q: 3. Prove that the lines x-9 +4 = 2-5 and 2 6x + 4y - 5z = 4,x - 5y + 2z = 12 are coplanar. Also find their point of intersection and the equation of the plane in which they lie.
Answer (1)
4th Aug, 2021
To prove that 2 lines are coplanar. We take two points A and B such that (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ) be the coordinates of the points respectively.
2)Then calculate the direction cosines of two vectors m1 and m2 is given by a1, b1, c1 and a2, b2, c2.
3)The two lines will be coplanar if you substitute the above found values in the condition- LM.(m1Xm2)=0 you will see that the LHS and RHS will both be 0 hence the lines will be coplanar.
4)When proved to be coplanar you can then easily find their equation and intersection.
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