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.
Answer:
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Step-by-step explanation:
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-2x-y=3 ...(1)
x+2y=4 ...(2)
multiply (2) by 2 and add to (1)
-2x-y+2x+4y=3+8
3y=11
y=11/3
from (2)
x=4-2y=4-2(11/3)
or x=4-(22/3)
=(12-22)/3=-10/3
Conversions: to smallest (inches)
n= 22 inches
b= 2 1/3 yard = 84 inches
t= 12 1/2 feet = 150 inches
total space = t
night stand = n (2n for two nightstands)
bed=b
b+2n has to be < or = to t
84+2(22)=x
84+44=128
128 is < 150
therefore the answer is yes they will fit with 22 inches left over.