[SOLVED] Vector Algebra (prove line lies on the plane)

**nameck** · December 7th 2009, 04:33 PM

hey there...
need guidance to solve my vector problem here.. =)
Let Rd = (a)i + (6)j + (1)k be the position vector of point D.
Determine the value of a so that D lies in the plane ABC
ABC plane => x + 6y -8z = 5

**Scott H** · December 7th 2009, 05:10 PM

In order that

$\mathbf{R}_D=a\mathbf{i}+6\mathbf{j}+\mathbf{k}$

point from the origin to a point on

$x+6y-8z=5,$

it is enough that the components of $\mathbf{R}_D$ satisfy the equation that defines the plane: that is, that

$a+6\cdot 6-8\cdot 1=5.$

**nameck** · December 7th 2009, 05:20 PM

what is the general equation for
(a x 1) + (6 x 6) + (8 x 1) = 5 ?

**Scott H** · December 7th 2009, 05:23 PM

Carrying out the multiplication, we obtain

$\begin{aligned}<br /> a+36-8&=5\\<br /> a+28&=5.\end{aligned}$

Now, we must solve for $a$ . Hint: we may do something to both sides of the equation.

**nameck** · December 7th 2009, 05:26 PM

a = -23?
am i correct?

**Scott H** · December 7th 2009, 05:31 PM

You are correct.

**nameck** · December 7th 2009, 06:12 PM

thanks Scott!! =)

Thread: [SOLVED] Vector Algebra (prove line lies on the plane)

LinkBack

Thread Tools

Display

[SOLVED] Vector Algebra (prove line lies on the plane)

Similar Math Help Forum Discussions

vector lies in the plane

Vector Algebra (line perpendicular to plane)

Help with easy Vector/Line/Plane problem

Proving this line lies on this plane with a specfic equaction

Verify that a line lies wholly in a plane

Search Tags