What is the vector of position of the intersection point of the lines d1 and d2? r=2i+j+m(i+3j) r=6i-j+n(i-4j)

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r= 2i + j + m(i+3j) .............(1)

r= 6i - j + n(i-4j)...............(2)

To find the point f intersection, then eq. (1) = eq.(2)

==> 2i + j + m(i+3j) = 6i - j + n(i-4j)

==>Let us expand brackets:

==> 2i + j + mi + 3mj = 6i - j + ni...

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r= 2i + j + m(i+3j) .............(1)

r= 6i - j + n(i-4j)...............(2)

To find the point f intersection, then eq. (1) = eq.(2)

==> 2i + j + m(i+3j) = 6i - j + n(i-4j)

==>Let us expand brackets:

==> 2i + j + mi + 3mj = 6i - j + ni - 4nj

==> (2+m) i + (1+3m)j = (6+n)i + (-1-4n)j

==> (2+ m - 6 - n)i + (1+3m +1 + 4n) j = 0

==> (-4+m-n) i + (2+3m+4n) = 0

==> -4 + m - n = 0

==> m= n+4

==> 3m + 4n+2= 0

==> 3(n+4) + 4n = -2

==> 3n + 12 + 4n =- 2

===> 7n = -14

==> n = -2

==> m = n+ 4 = -2 + 4 = 2

==> m= 2

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