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
Jim G.
Sep 21, 2017

#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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