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Question

Show that the lines ¯¯¯r=(^i+^j^k)+λ(3^i^j) and ¯¯¯r=(4^i^j)+μ(2^i^3k) intersect. Find their point of intersection.

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Solution

Given line are

¯¯¯r=(ˆi+ˆjˆk)+λ(3ˆiˆj)and¯¯¯r=(4ˆiˆj)+μ(2ˆi3ˆk)

These two line will be intersect if their correspondent coefficient are equal

¯¯¯r=(ˆi+ˆjˆk)+λ(3ˆiˆj)and¯¯¯r=(4ˆiˆj)+μ(2ˆi3ˆk)ˆi(1+3λ)+ˆj(1λ)+ˆk(1)=ˆi(4+2μ)+ˆj(1)+ˆk(3μ)so1λ=1λ=21+3λ=4+2μ1+3(2)4=2μμ=32putλ=2¯¯¯r=(ˆi+ˆjˆk)+2(3ˆiˆj)=7ˆiˆjˆk

Point of intersection is (7 , -1 -1 )






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