How to find area of triangle with two vertices?

**henrymath** · March 15th 2010, 01:55 PM

How do I find the area of a triangle with two sides given by a = <1,3,-1> and b = <2,-1,2>? Thank you.

**skeeter** · March 15th 2010, 02:01 PM

Originally Posted by henrymath

How do I find the area of a triangle with two sides given by a = <1,3,-1> and b = <2,-1,2>? Thank you.

what does $|\vec{a} \times \vec{b}|$ get you?

**henrymath** · March 15th 2010, 03:34 PM

Originally Posted by skeeter

what does $|\vec{a} \times \vec{b}|$ get you?

I get
a x b = 5i - 4j - 7k

**skeeter** · March 15th 2010, 04:18 PM

Originally Posted by henrymath

I get
a x b = 5i - 4j - 7k

the magnitude of the cross product of two vectors is the area of the parallelogram formed with the two vectors as adjacent sides.

triangle area = 1/2 parallelogram area

**henrymath** · March 16th 2010, 07:04 PM

Originally Posted by skeeter

the magnitude of the cross product of two vectors is the area of the parallelogram formed with the two vectors as adjacent sides.

triangle area = 1/2 parallelogram area

Thanks. my answer was 1/2 sqrt 90.

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