Question

Find the area of a triangle formed by placing the vectors [3, 6] and [7, 1] tail-to-tail.

(Continuation) Describe your triangle using a different pair of vectors.

(Continuation) Find the length of the longest altitude of your triangle.

Answer 1

a.
`A=10u^(2)`

b. View graph

c. 6.40u

Explanation:

knowing that the triangle area is equal to base by heigh between two, then:

`A=(bh)/(2)=(5*4)/(2)=10u^(2)`

The length of the longest altitude of your triangle is:

`c^(2)=a^(2)+b^(2)=5^(2)+4^(2)=25+16=41\\ c=√(41)=6.40u`

finally it can be seen that the position of the triangle does not matter, as long as the base and heigh are maintained, the area of ​​the triangle will be the same