Given that |vec(n)|=1,|vec(m) |=sqrt(3) And that the angle between the vectors |vec(m)| and |vec(n)| is 30^(circ). We will define vec(a) =vec(m)−vec(n) , vec(b) =vec(m) +vec(n) calculate the area of ​​the triangle created by vectors vec(a) ,vec(b).

Javion Henry 2022-07-21 Answered
Given that | n | = 1 , | m | = 3 And that the angle between the vectors | m | and | n | is 30
We will define a = m n , b = m + n calculate the area of ​​the triangle created by vectors a , b
I found out what | a | and | b | but not sure how to continue form here.
| a | 2 = ( m n ) ( m n ) = | m | 2 2 m n + | n | 2 = 3 2 3 1 3 2 + 1 = 1 | a | = 1
| b | 2 = ( m + n ) ( m + n ) = | m | 2 + 2 m n + | n | 2 = 3 + 2 3 1 3 2 + 1 = 7 | b | = 7
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Answers (1)

abortargy
Answered 2022-07-22 Author has 19 answers
The area of triangle generated by u and v is 1 2 | u × v | = 1 2 | u | | v | sin θ
θ is 30 degree.
a × b = ( x y ) × ( x + y ) = x × x + x × y y × x y × x = 2 x × y
So the area of triangle generated a and b is twice of area of triangle generated x and y .
So the answer is | x | | y | sin $ 30 = 3 2
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