Vectors

The question I have a problem with is this:

1. The lines l1 and l2 have vector equations given by:

r1 = 3i - j + 2k + λ(-2i + j + k)
r2 = -2i + 9j - 2k + μ(5i - 2j + k)

Find the values of λand μ when the vector r1 - r2 is perpendicular to both lines.

2. Find the shortest distance between the two lines
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I am getting the values of λand μ both zero, and I do not think it makes sense, since you wouldn't be able to work out part 2.

Any help?

Thanks in advance

Quote:

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Originally Posted by yobacul

The question I have a problem with is this:

1. The lines l1 and l2 have vector equations given by:

r1 = 3i - j + 2k + λ(-2i + j + k)
r2 = -2i + 9j - 2k + μ(5i - 2j + k)

Find the values of λand μ when the vector r1 - r2 is perpendicular to both lines.

2. Find the shortest distance between the two lines

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As stated, this question makes no sense.
Let .
The vector is perpendicular to both lines.
The distance between the two lines is .