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Question
The lines `vecr = hati + hatj - hatk + λ(2hati + 3hatj - 6hatk)` and `vecr = 2hati - hatj - hatk + μ(6hati + 9hatj - 18hatk)`; (where λ and μ are scalars) are ______.
Options
coincident
skew
intersecting
parallel
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Solution
The lines `vecr = hati + hatj - hatk + λ(2hati + 3hatj - 6hatk)` and `vecr = 2hati - hatj - hatk + μ(6hati + 9hatj - 18hatk)`; (where λ and μ are scalars) are parallel.
Explanation:
Vectors `2hati + 3hatj - 6hatk` and `6hati + 9hatj - 18hatk` are parallel and the fixed point `hati + hatj - hatk` on the line `vecr = hati + hatj - hatk + λ(2hati + 3hatj - 6hatk)` does not satisfy the other line `vecr = 2hati - hatj - hatk + μ(6hati + 9hatj - 18hatk)`; where λ and μ are scalars.
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