Question

prove that if A,B AND are three points in space,then the area of triangle ABC can be calculated with formula : Area of triangle ABC =1/2 absolute AB*AC.

Answer 1

uhm, that would be the cross-product of vectors AB and AC.

Answer 2

HOW

Answer 3

can we assume this? \[\huge \left| A \times B \right|=\left| A \right| \left| B \right| \sin \theta \]

Answer 4

YES

Answer 5

\[\large \left| AB \right|\]is the length of vector AB and \[\large \left| AC \right|\] is the lengthh of AC, while theta is the angle formed by the two vectors.
the area of a side-angle-side triangle is \[\large \frac{ 1 }{ 2 } ab \sin \theta\]

Answer 6

\[\large \frac{ 1 }{ 2 }\left| AB \times AC \right|=\frac{ 1 }{ 2 }\left| AB \right|\left| AC \right| \sin \theta\] and the right side of the equation is the area of the triangle.

Answer 7

WHAT ABOUT IF YOU DONT ASSUME?

Answer 8

then we'll have to prove it.

Answer 9

CAN YOU DO IT?

Answer 10

most textbooks include a proof of \[\large \left| AB \times AC \right|=\left| AB \right|\ \left| AC \right| \sin \theta\] so i leave reading the proof to you.