MarkFL said:Hello, and welcome to MHB, Gummg! (Wave)
I would write the plane's velocity vector as:
\(\displaystyle \vec{v}=485\left\langle \cos\left(117^{\circ}\right),-\sin\left(117^{\circ}\right) \right\rangle\)
And the wind's velocity vector as:
\(\displaystyle \vec{w}=35\left\langle \cos\left(162^{\circ}\right),\sin\left(162^{\circ}\right) \right\rangle\)
And so the resultant ground speed vector will be the vector sum:
\(\displaystyle \vec{r}=\vec{v}+\vec{w}\)
Can you proceed?
Gummg said:How did you get 117 and 162 degrees?
A vector is a quantity that has both magnitude (size or length) and direction. It is often represented as an arrow in a coordinate system.
To add or subtract vectors, you can use the parallelogram method or the head-to-tail method. In both methods, you align the vectors with their tails at the same point and then draw a parallelogram or a triangle to find the resulting vector.
The dot product of two vectors is a scalar quantity that represents the projection of one vector onto the other. It is calculated by multiplying the magnitudes of the two vectors and then multiplying it by the cosine of the angle between them.
The cross product of two vectors is a vector that is perpendicular to both of the original vectors. It is calculated by multiplying the magnitudes of the two vectors and then multiplying it by the sine of the angle between them. The direction of the resulting vector is determined by the right-hand rule.
Vectors are used in various fields such as physics, engineering, and computer graphics. They can be used to represent forces, velocities, and other physical quantities. They are also used in navigation, such as determining the direction and distance of travel. In computer graphics, vectors are used to represent 3D objects and their movements.