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Question
Lines →r=(3+t)^i+(1−t)^j+(−2−2t)^k, t∈R and x=4+k, y=−k, z=−4−2k, k∈R then relation between lines is ______
Lines →r=(3+t)^i+(1−t)^j+(−2−2t)^k, t∈R and x=4+k, y=−k, z=−4−2k, k∈R then relation between lines is ______
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Solution
The correct option is B coincident
→r=(3^i+^j−2^k)+t(^i−^j−2^k), t∈R is a line passing through the point (3,1,−2) and parallel to the vector ^i−^j−2^k
Second line:
x−41=y−1=z+4−2=k, k∈R
Both lines have same direction ratios.
So, both lines are parallel.
Also (3,1,−2) lies on the second line.
Therefore, both lines are coincident.
→r=(3^i+^j−2^k)+t(^i−^j−2^k), t∈R is a line passing through the point (3,1,−2) and parallel to the vector ^i−^j−2^k
Second line:
x−41=y−1=z+4−2=k, k∈R
Both lines have same direction ratios.
So, both lines are parallel.
Also (3,1,−2) lies on the second line.
Therefore, both lines are coincident.
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