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Further vectors

The planes 1 and 2 have the cartesian equations given by 2x+y-3z=1 and 3x-4y+5z=6 respectively.
(a) Find, in degrees to one decimal place, the acute angle between the planes.
For this I used the dot product of the two normal vectors to get an angle of 71.6 degrees- is this correct?
(b) The two planes intersect to give a line L. Find a vector that is in the direction of L.
For this I did the vector product of the two normals to the planes to get 7i-19j-11k. Again, could someone confirm this is correct?
(c) Find an equation of the line L, giving your answer in the form (r-p)xq=0
I'm not sure how to do this one
(d) State the direction cosines of the line L
I have no idea how to do this??

Thanks in advance :smile:
Reply 1
Original post by aj9999
The planes 1 and 2 have the cartesian equations given by 2x+y-3z=1 and 3x-4y+5z=6 respectively.
(a) Find, in degrees to one decimal place, the acute angle between the planes.
For this I used the dot product of the two normal vectors to get an angle of 71.6 degrees- is this correct?
(b) The two planes intersect to give a line L. Find a vector that is in the direction of L.
For this I did the vector product of the two normals to the planes to get 7i-19j-11k. Again, could someone confirm this is correct?
(c) Find an equation of the line L, giving your answer in the form (r-p)xq=0
I'm not sure how to do this one
(d) State the direction cosines of the line L
I have no idea how to do this??

Thanks in advance :smile:

a,b) right method, but post working if you want it checked. Think your cross has one sign error.
c) http://www.math.pitt.edu/~sparling/23012/*vectors5/node23.html
d) try normalizing the vector?
https://onlinemschool.com/math/library/vector/cos/
(edited 3 years ago)

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