Question

Vector u and vector v are inclined at an angle of 30° with the positive x-axis.

If ||ul|=3√5 units and ||v|| = 4√5 units, then ||uv||-
=
units.

Answer 1

Using the law of cosines, we can find the magnitude of the vector uv as follows:

||uv||^2 = ||u||^2 + ||v||^2 - 2||u|| ||v|| cos(30°)

Substituting the given values, we get:

||uv||^2 = (3√5)^2 + (4√5)^2 - 2(3√5)(4√5) cos(30°)

Simplifying, we get:

||uv||^2 = 75 + 80 - 120
||uv||^2 = 35

Taking the square root of both sides, we get:

||uv|| = √35 units.

Therefore, the magnitude of the vector uv is √35 units.