# Thread:

1. ## Vectors!

HI I want to check if my answers are right here, I can't do the last part so I believe my answers in the previous parts must be wrong..

Points A,B,C,D have the following coordinates
A1,3,1) B1,2,4) C2,3,6) D5,-2,1)

ai.) Evaluate the vector product, giving your answers in terms of the unit vectors i,j,k.

I found AB and AC and got -5i, 3j and 1k from doing the cross product.

aii.) Find the area of the triangle ABC.

I took the magnitude of the cross product result in ai.) and halved it, getting (1/2)sqrt(35)units^2

b.) The plane containing the points A,B, C is denoted by pi and the line passing through D perpendicular to pi is denoted by L. The point of intersection of L and pi is denoted by P.

bi.) FInd the cartesian equation of pi.

AB is the direction vector of pi, I thought. And then I'll need a point so
I got x=1, y=3-t, z=1+3t

bii.) FInd the cartesian equation of L.

The result of the cross product in ai.) is the direction vector of L, I thought. Dotting it by the direction vector of pi, I will get a zero.
So my answer was
x=5-5t, y=-2+3t, z=1+t

c.) Find the coordinates of P.

This is where I know my previous answers are wrong. I though to equate all the x, y and z values of L and pi. I get different values for t each time...

Please help me out!

Thank you!

2. ## Re: Vectors!

Did you get a satisfactory answer to your question? I can help you on this - but I'm not going to if you already have a solution. The post has been here a while and I just joined the site.

3. ## Re: Vectors!

Originally Posted by Tutu
HI I want to check if my answers are right here, I can't do the last part so I believe my answers in the previous parts must be wrong..

Points A,B,C,D have the following coordinates
A1,3,1) B1,2,4) C2,3,6) D5,-2,1)

ai.) Evaluate the vector product, giving your answers in terms of the unit vectors i,j,k.

I found AB and AC and got -5i, 3j and 1k from doing the cross product.

aii.) Find the area of the triangle ABC.

I took the magnitude of the cross product result in ai.) and halved it, getting (1/2)sqrt(35)units^2
Yes, this is correct.

b.) The plane containing the points A,B, C is denoted by pi and the line passing through D perpendicular to pi is denoted by L. The point of intersection of L and pi is denoted by P.

bi.) FInd the cartesian equation of pi.

AB is the direction vector of pi, I thought. And then I'll need a point so
I got x=1, y=3-t, z=1+3t
I don't undertand what you are saying here. You were asked for an equation of the plane, pi. This is the parametric equations for a line, not a plane.

bii.) FInd the cartesian equation of L.

The result of the cross product in ai.) is the direction vector of L, I thought. Dotting it by the direction vector of pi, I will get a zero.
So my answer was
x=5-5t, y=-2+3t, z=1+t
Yes, this is correct.

[qote]c.) Find the coordinates of P.

This is where I know my previous answers are wrong. I though to equate all the x, y and z values of L and pi. I get different values for t each time...

Please help me out!

Thank you![/QUOTE]
The equation of a plane, with normal vector <A, B, C> and containing point [tex](x_0, y_0, z_0)[tex] is $A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0$.
You can use that to answer (bi) and then replace x, y, and z in the equation of the plane with the x, y, and z from (bii) to get a single equation to solve for t.

#### Search Tags

Copyright © 2005-2013 Math Help Forum. All rights reserved.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9261181354522705, "perplexity_flag": "middle"}