Help with finding variables in vectors?

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Help with finding variables in vectors?

Relative to an origin $O$ , the position vectors of points $A$ , $B$ and $C$ are given by

$vec(OA) = (0, 2, -3)$
$vec(OB) = (2, 5, -2)$
$vec(OC) = (3, p, q)$

In the case where angle $ABC$ is a straight line, find the values of $p$ and $q$ .

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Answer 1 · 2017-09-21T18:18:10

$p=13/2,q=-3/2$

Explanation:

$"since A, B and C all lie in a straight line"$

$"then they are "color(blue)"colinear"$

$rArrvec(BC)=kvec(AB)larr" k is a scalar"$

$vec(AB)=ulb-ula=((2),(5),(-2))-((0),(2),(-3))=((2),(3),(1))$

$vec(BC)=ulc-ulb=((3),(p),(q))-((2),(5),(-2))=((1),(p-5),(q+2))$

$"to find k we can only use the direction values of the"$
$"x-components"$

$"that is "2to1rArrk=1/2$

$rArrp-5=3/2rArrp=13/2$

$rArrq+2=1/2rArrq=-3/2$

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Help with finding variables in vectors?

Relative to an origin $O$ , the position vectors of points $A$ , $B$ and $C$ are given by

$vec(OA) = (0, 2, -3)$
$vec(OB) = (2, 5, -2)$
$vec(OC) = (3, p, q)$

In the case where angle $ABC$ is a straight line, find the values of $p$ and $q$ .

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

Help with finding variables in vectors?

Relative to an origin OO, the position vectors of points AA, BB and CC are given by vec(OA) = (0, 2, -3)vec(OA) = (0, 2, -3) vec(OB) = (2, 5, -2)vec(OB) = (2, 5, -2) vec(OC) = (3, p, q)vec(OC) = (3, p, q) In the case where angle ABCABC is a straight line, find the values of pp and qq.

1 Answer

Explanation:

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Impact of this question

Relative to an origin $O$ , the position vectors of points $A$ , $B$ and $C$ are given by

$vec(OA) = (0, 2, -3)$
$vec(OB) = (2, 5, -2)$
$vec(OC) = (3, p, q)$

In the case where angle $ABC$ is a straight line, find the values of $p$ and $q$ .