find the vector with all of the following properties:

magnitude 10
angle of 45 degrees with positive x-axis
angle of 75 with positive y-axis
positive k component

r= 10cos45 i + 10 cos75 j + Z k

but you know you can find Z by this

10^2=10^2*cos^2 45 + 10^2 cos^2 75 + Z^2

or

Z= 10 sqrt (1-.5-.067)
Z= 6.58

check all that.

thank you so much

so then is the vector .5i + .067j + 6.58k??

To find a vector with the given properties, follow these steps:

1. Start by visualizing a coordinate plane.
2. Draw the positive x-axis and the positive y-axis.
3. From the origin (0,0), draw a vector with a magnitude of 10 units and an angle of 45 degrees with the positive x-axis. This will create a vector that is 45 degrees above the x-axis.
4. Next, draw a line parallel to the positive y-axis from the end of the first vector and another vector with an angle of 75 degrees with the positive y-axis. This will create a vector that is 75 degrees from the positive y-axis.
5. Lastly, connect the end of the second vector to the z-axis with a positive k component. This will create a vector that satisfies all of the given properties.

Note: The k component refers to the third coordinate in a 3D space, commonly known as the z-axis in a three-dimensional coordinate system. If you are working in a two-dimensional space, you can ignore the k component and consider it as 0.

Please note that there can be multiple vectors that satisfy these properties, as the starting point (origin) of the vector is not specified.