Question

Vectors Question - Help?
I have solved part (i) where the positional vector is = 13/2i - 3/2j + 1/2k

But I'm stuck on part (ii), I'm not too sure what to do. Do I use scalar product or what?

Answer 1

do you still need help?

Answer 2

@alekos
Preferably, but it is already really late now so I need to go to sleep. Maybe you could give me the first few steps or set me in a direction and I'll try it tomorrow?

Answer 3

For (ii), there may be some tricky way to solve with "vector stuff", but off-hand I don't see it. However, we can do it with algebra on the components.
we want to find \( \vec{N} = < 1, b,c>\), so that for point \( \vec{P} \)
\[ \vec{N} \cdot \vec{P} = d \]
b, c and d to be determined.

We are given
\[ <1, b, c> \cdot <2, -3, 2> = d \\ <1, b, c> \cdot <5, -2, 1> = d \]
use that pair to solve for e.g. c in terms of b

also, the normals of the two planes are 60º (or 120º , it's ambiguous when they say the planes form an "acute angle of 60º )
\[ <1, b, c> \cdot < 1, 1 , 0> = \sqrt{1+b^2 + c^2} \sqrt{2} \cos(60) \]
replace c (from the first step), and solve for b
and then c
finally, sub in point A or B into the equation for the plane to find d

Answer 4

btw, if the post is not readable, re-fresh your browser.

Answer 5

***also, the normals of the two planes are 60 degrees ***
should be
the normals of the two planes form a 60 degree angle.