Vectors in three dimensions

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1141

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Can anybody help me?

The question is:

The point A, B, and C have position vectors a = (2,1,2) , b = (-3,2,5) and c = (4,5,-2) respectively, with respect to a fixed origin. The point D is such that ABCD, in that order, is a parallelogram.

a.) Find the position vector of D.
b.) Find the position vector of the point at which the diagonals of the parallelogram intersect.
c.) Calculate the angle BAC, giving your answer to the nearest tenth of a degree


So, I've having trouble starting question a.) and I'm not sure how I would go about doing question b.). But question c.) I can definitely do, no problem with that.
 
1141 said:
Can anybody help me?

The question is:

The point A, B, and C have position vectors a = (2,1,2) , b = (-3,2,5) and c = (4,5,-2) respectively, with respect to a fixed origin. The point D is such that ABCD, in that order, is a parallelogram.

a.) Find the position vector of D.
b.) Find the position vector of the point at which the diagonals of the parallelogram intersect.
c.) Calculate the angle BAC, giving your answer to the nearest tenth of a degree


So, I've having trouble starting question a.) and I'm not sure how I would go about doing question b.). But question c.) I can definitely do, no problem with that.
Click to expand...

This problem can be solved many ways. One such way:

Let the position vector of D be (d1, d2, d3)

Impose AB||CD and AC||BD

Then impose AB = CD

That should provide you with enough information to solve for (d1, d2, d3)
 
1141 said:
Can anybody help me?

The question is:

The point A, B, and C have position vectors a = (2,1,2) , b = (-3,2,5) and c = (4,5,-2) respectively, with respect to a fixed origin. The point D is such that ABCD, in that order, is a parallelogram.

a.) Find the position vector of D.
b.) Find the position vector of the point at which the diagonals of the parallelogram intersect.
c.) Calculate the angle BAC, giving your answer to the nearest tenth of a degree
Click to expand...
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Part b) In a parm the diagonals bisect each other,so the intersection of the diagonals is the midpoint of one of the diagonals . . .

Position vector , then you must take it with respect to O(origin) >l: Just get V(OI) . . .

Part C ) Let's see an attempt from you . . .
 
You can do the part (a) using vectors.

Hints:

Vector AB + vector AC = vector AD

position vector OA + vector AD = position vector OD
 
You can also find three distance formula equations that involve the three coordinates for point D.
 
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