Answer:
Step-by-step explanation:
Given that L is a line parametrized by

The plane perpendicular to the line will have normal as this line and hence direction ratios of normal would be coefficient of t in x,y,z
i.e. (2,3,-1)
So equation of the plane would be of the form

Use the fact that the plane passes through (2,0,-1) and hence this point will satisfy this equation.

So equation is

b) Substitute general point of L in the plane to find the intersecting point

i.e. same point given.
I have geometry to but i didn’t get to that yet sorry
let h= history books
science books = s
h=2s there are 2 times as many history as science so to get them equal we double the science
h+s=81 there are 81 total history and science books
2s+s=81 substitute 2s for h in the above equation
3s = 81 combine like terms
s = 27
There are 27 science books
h=2s
h=2(27)
h=54
there are 54 history books
Answer:
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