It is a vector question?
1 Answer
May 1, 2018
# p= 6.5 \ \ # , and#q= -1.5# ,
Explanation:
We have:
# bbvec(OA) = ((0),(2),(-3)) \ \ # ,# bbvec(OB) = ((2),(5),(-2)) \ \ # and# bbvec(OC) = ((3),(p),(q)) #
And so we can compute the vector
# bbvec(AB) = bbvec(OB) - bbvec(OA) = ((2),(5),(-2)) - ((0),(2),(-3)) = ((2),(3),(1)) #
Similarly, we can compute the vector
# bbvec(BC) = bbvec(OC) - bbvec(OB) = ((3),(p),(q)) - ((2),(5),(-2)) = ((1),(p-5),(q+2)) #
As ABC is a straight line then, for some constant
# bbvec(AB) = lamda bbvec(BC)#
Hence we have:
# ((2),(3),(1)) = lamda ((1),(p-5),(q+2)) #
Equating components:
# R1: 2 = lamda# ,
# R2: 3=lamda(p-5) => p-5=3/2 => p= 6.5# ,
# R3: 1=lamda(q+2) => q+2=1/2 => q= -1.5# ,