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

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

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

2. In order that

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

point from the origin to a point on

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

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

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

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

4. Carrying out the multiplication, we obtain

\displaystyle \begin{aligned} a+36-8&=5\\ a+28&=5.\end{aligned}

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

5. a = -23?
am i correct?

6. You are correct.

7. thanks Scott!! =)

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# how to determine if a line lies in a plane

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