# Math Help - 2 vector calc questions

1. ## 2 vector calc questions

consider points p(2,1,3), q(1,2,1), R(-1,-1,-2), s(1,-4,0)
Find the shortest distance between lines pq and rs

Find the constant a so that the following vectors are coplanar
2i-j+k i+2j-3k 3i-j+2k

consider points p(2,1,3), q(1,2,1), R(-1,-1,-2), s(1,-4,0)
Find the shortest distance between lines pq and rs
Is it clear to you these two lines are skew lines?
The distance between two skew lines, $P + t\overrightarrow d \,\& \,R + s\overrightarrow e$ then the distance between them is:
$\frac{{\left| {\overrightarrow {PR} \cdot \left( {\overrightarrow d \times \overrightarrow e } \right)} \right|}} {{\left\| {\overrightarrow d \times \overrightarrow e } \right\|}}$

4. i dont understand

i dont understand
Well if that is truly the case, do you think that you are ready to do this problem?

6. im not familiar with the notation u used
what do the double bars in the denominator mean

im not familiar with the notation u used
what do the double bars in the denominator mean
Magnitude. Of course I'm also assuming he means the same with the single bars in the top. It essentially is the exact same thing as an "absolute value" sign.

As for your second question, for three vectors to be coplanar, their scalar triple product must be 0. My problem, is I see no constant "a" in any of those vectors that one would have to solve for. Is their information missing from the problem.

8. The reason for the single bars on top is that the dot product is a number

hence we have the absolute value of a number.

On the bottom we have double bars because the cross product is a vector so we can talk about the magnitude of a vector but not the absolute value of a vector.

9. for the answer to this question i keep getting 16/square root of 53

but the answer in the book is the 3root 2
can someone confirm that i am right and the book is wrong this is driving me crazy

10. could someone confirm i am doing this right