Vector problem

**Paymemoney** · January 21st 2010, 01:36 AM

HI
Can someone tell me how would i complete the following question:

If $a=2i-3j+k, b=2i-4j+5k$ and $c=-i-4j+2k$ find the values of p and q such that a+pb+qc is parallel to the x-axis.

This is what i just started:
$2i-3j+k+p(2i-4j+5k)+q(-i-4j+2k)<br />$
P.S

**Prove It** · January 21st 2010, 03:14 AM

Originally Posted by Paymemoney

HI
Can someone tell me how would i complete the following question:

If $a=2i-3j+k, b=2i-4j+5k$ and $c=-i-4j+2k$ find the values of p and q such that a+pb+qc is parallel to the x-axis.

This is what i just started:
$2i-3j+k+p(2i-4j+5k)+q(-i-4j+2k)<br />$
P.S

If the resultant vector is parallel to the $x$ axis, then its $\mathbf{j}$ and $\mathbf{k}$ components are 0.

**Paymemoney** · January 21st 2010, 02:48 PM

the answers says $p=\frac{1}{6}$ and $q=\frac{-11}{12}$

**Prove It** · January 21st 2010, 08:02 PM

Do what I said.

Collect the $\mathbf{i},\mathbf{j}$ and $\mathbf{k}$ terms.

Set the $\mathbf{j}$ and $\mathbf{k}$ terms to 0.

Solve the resulting equations.

**Paymemoney** · January 21st 2010, 09:27 PM

ok i'll tried that

**Paymemoney** · January 22nd 2010, 12:01 AM

I still cannot get it can someone tell me the working to this.

**bryankek** · January 22nd 2010, 12:28 AM

continuing from where u left off

$<br /> 2\mathbf{i}-3\mathbf{j}+\mathbf{k}+p(2\mathbf{i}-4\mathbf{j}+5\mathbf{k})+q(-\mathbf{i}-4\mathbf{j}+2\mathbf{k})=(2+2p-2q)\mathbf{i}-(3+4p+4q)\mathbf{j}+(1+5p+2q)\mathbf{k}<br />$

as stated in the question, the vector a+pb+qc is parallel to the x-axis

therefore, the $\mathbf{j}$ and $\mathbf{k}$ component are null
using that result;

$3+4p+4q = 0$ --> (1)
$1+5p+2q = 0$ --> (2)

(2) multiply by 2

$2+10p+4q=0$ --> (2a)

(2a)-(1);

$-1+6p = 0$
$p = \frac{1}{6}$

substitute $p = \frac{1}{6}$ into (1)
$q = \frac{-11}{12}$

Thread: Vector problem

LinkBack

Thread Tools

Display

Vector problem

Similar Math Help Forum Discussions

A vector problem.

Vector Problem

Gr 12. Vector problem!

A Vector Problem

Vector Problem

Search Tags