Hi

I have a question regarding vectors and how to solve problems given a set of points forming a triangle.

"For triangle ABC, with vertices A=(1,2,2), B=(0,-2,1) and C=(1,5,-1) find:

(a) the length of side AB - I have done this;

(b) the equation of the line that passes through A & B - we went through finding equations using parametric, vector and symmetric form however focussed on 3-space. To find the equation of the line that passes through A&B do I just use the x and y coordinates? When we looked at it we only used the three coordinates when finding the equation of a plane.

I then have two sets of equations:r=r(1) + t(r(2)-r(1); and

t=x-x(1)/x(2)-x(1) = y-y(1)/y(2)-y(1)

(I have used brackets to denote subscripts in the above)

So do I use the second formula to find t and then put that into the first equation.Please let me know if I am completely lost.

(c) the angle at vertex B - I assume I find the magnitude of AB and BC and then use the cos theta formula?

(d) a vector perpendicular to the plane containing the triangle ABC - is this the cross product of AB, BC and CA?

(e) the area of the triangle ABC - in order to do this do I need to find the component of one vector in relation to another - to form a right angled triangle with height being the component found?

Kind regards

Beetle

I have a question regarding vectors and how to solve problems given a set of points forming a triangle.

"For triangle ABC, with vertices A=(1,2,2), B=(0,-2,1) and C=(1,5,-1) find:

(a) the length of side AB - I have done this;

(b) the equation of the line that passes through A & B - we went through finding equations using parametric, vector and symmetric form however focussed on 3-space. To find the equation of the line that passes through A&B do I just use the x and y coordinates? When we looked at it we only used the three coordinates when finding the equation of a plane.

I then have two sets of equations:r=r(1) + t(r(2)-r(1); and

t=x-x(1)/x(2)-x(1) = y-y(1)/y(2)-y(1)

(I have used brackets to denote subscripts in the above)

So do I use the second formula to find t and then put that into the first equation.Please let me know if I am completely lost.

(c) the angle at vertex B - I assume I find the magnitude of AB and BC and then use the cos theta formula?

(d) a vector perpendicular to the plane containing the triangle ABC - is this the cross product of AB, BC and CA?

(e) the area of the triangle ABC - in order to do this do I need to find the component of one vector in relation to another - to form a right angled triangle with height being the component found?

Kind regards

Beetle

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