Answer to Question #88315 in Analytic Geometry for Shivam Nishad

Question #88315
A, B, C, D are the points i − k, − i + 2 j, 2i − 3k, 3i − 2 j − k respectively. Show that the
projection of AB on CD is equal to that of CD on AB . Also find the cosine of their inclination.
1
Expert's answer
2019-04-29T10:35:58-0400

1.

A(1;0;-1)

B(-1;2;0)

C(2;0;-3)

D(3;-2;-1)

Then

"\\overrightarrow{AB}=(-1-1;2-0;0+1)=(-2;2;1)"

"\\overrightarrow{CD}=(3-2;-2-0;-1+3)=(1;-2;2)"

The projection AB on CD is:


"\\overrightarrow{AB}\\cdot\\overrightarrow{CD}\/|CD|=(-2-4+2)\/\\sqrt{1\u00b2+(-2)\u00b2+2\u00b2}=-4\/3"

The projection CD on AB is:

"\\overrightarrow{CD}\\cdot\\overrightarrow{AB}\/|AB|=(-2-4+2)\/\\sqrt{(-2)\u00b2+2\u00b2+1\u00b2}=-4\/3"

Then the projection AB on CD is equal to the projection CD on AB

2.


"cos(\\overrightarrow{AB},\\overrightarrow{CD})=\\overrightarrow{AB}\\cdot\\overrightarrow{CD}\/(|AB|\\cdot|CD|)="

"=(-2-4+2)\/\\sqrt{1\u00b2+(-2)\u00b2+2\u00b2}\\cdot\\sqrt{(-2)\u00b2+2\u00b2+1\u00b2}=-4\/9"



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS