Vectors: Find MP in terms of a, b, and c

[velocity06]

Hi everyone,

I kind ask you to please check my work for the following question:

Find in terms of a,b and c (vector MP)

P,M and N are midpoints

Vector MP:

MP = MO + OP
= (OC + 1/2(CA)) + 1/2(OB)
= c + 1/2(-a+c) + 1/2(b)

Am I on the right path?

Thank you for your help!

 

[Dr.Peterson]

Find in terms of a,b and c (vector MP)

P,M and N are midpoints

Vector MP:

MP = MO + OP
= (OC + 1/2(CA)) + 1/2(OB)
= c + 1/2(-a+c) + 1/2(b)

Am I on the right path?

Thank you for your help!

Very close. But OC + 1/2(CA) = OM, not MO; and CA is OA - OC = a - c, not -a + c. So you are on the right path, but going the wrong direction sometimes!

(I'm assuming that a is defined as the vector OA, and so on.)

 

[velocity06]

Thanks Dr. Petersen

Here is my solution:

MP = MO + OP
= (MA + AO) + OP
= 1/2(CA) + (-a) + 1/2(OB)
= 1/2(CO + OA) -a +1/2(b)
= 1/2(-c+a) -a+1/2(b)
= -1/2(c)+1/2(a)-a+1/2(b)
= -1/2(c)-1/2(a)+1/2(b)
= 1/2(b-a-c)
= 1/2(b-(a+c))

Regards,

 

[Dr.Peterson]

Here is my solution:

MP = MO + OP
= (MA + AO) + OP
= 1/2(CA) + (-a) + 1/2(OB)
= 1/2(CO + OA) -a +1/2(b)
= 1/2(-c+a) -a+1/2(b)
= -1/2(c)+1/2(a)-a+1/2(b)
= -1/2(c)-1/2(a)+1/2(b)
= 1/2(b-a-c)
= 1/2(b-(a+c))

Regards,

Looks good!