Vectors

sojeee

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Oct 24, 2017
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Points A and B have position vectors a and b. O is the origin and point P is such that OAPB is a parallelogram.
a) Write down the position vector of P in terms of a and b.
b) Find position vector of M, the midpoint of AP.
Point Q lies on the vector OP. Let vector OQ=t (vector)OP
c) Express vector BQ in terms of t, a and b. Hence, find the value of t for which BQM is a straight line.

a) Vector OP = a + b
b) Vector OM = a + 1/2b
c) Vector BQ = -b + ta + tb
Vector QM = -a -b + a + 1/2b

-1 + t = -1/2
t = 1/2

I got t wrong and don't know what else to do.
 
Points A and B have position vectors a and b. O is the origin and point P is such that OAPB is a parallelogram.
a) Write down the position vector of P in terms of a and b.
b) Find position vector of M, the midpoint of AP.
Point Q lies on the vector OP. Let vector OQ=t (vector)OP
c) Express vector BQ in terms of t, a and b. Hence, find the value of t for which BQM is a straight line.

a) Vector OP = a + b
b) Vector OM = a + 1/2b
c) Vector BQ = -b + ta + tb
Vector QM = -a -b + a + 1/2b

-1 + t = -1/2
t = 1/2

I got t wrong and don't know what else to do.

Your QM is clearly wrong, as it must depend on t. Try that again.
 
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