Question

Help i just want to know if it's right or wrong

Answer 1

Step-by-step explanation

We consider a vector with:

• initial point (x₁, y₁) = (4, 3),

,

• final point (x₂, y₂) = (-4, -1).

The magnitude of the vector is given by:

`||v||=√((x_2-x_1)^2+(y_2-y_1)^2)=√((-4-4)^2+(-1-3)^2)\cong8.944.`

The angle of the vector is given by:

`\tan\theta^(\prime)=(y_2-y_1)/(x_2-x_1)=(-1-3)/(-4-4)=(-4)/(-8)=(1)/(2)\Rightarrow\theta^(\prime)=\tan^(-1)((1)/(2))\cong26.565.`

We have obtained a positive value of the angle θ'. But we see that our vector points in the negative direction. To take into account this, we must sum 180° to this result:

`θ\cong26.565\degree+180\degree=206.565\degree.`Answer

||v|| = 8.944, θ = 206.565°