# Vector problems with solution

Problem statement:

Given the vectors: A = 3i + 2jk and B = 5i +5j.
Determine:

1. Their magnitude.
2. The direction of B.
3. A + B
4. A -2 B
5. A unit vector parallel to A.
6. A vector of magnitude 2 and opposite to B

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Solution:

It is essential when working with vectors to use proper notation. Always draw an arrow over the letters representing vectors. You can also use bold characters to represent a vector quantity.
Vectors A and B are written using the unit vector notation.
The magnitude of A is given by: Similarly, the magnitude of B is: The magnitude of a vector is always a positive number.

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In the figure below vector B is shown, as well as the standard unit vectors (in red). As we saw when we first introduced the scalar and vector quantities, we can derive the polar components of a vector from the Cartesian coordinates: The vector sum of A and B is given by: In order to solve section (d) we multiply B by -2 and then we add A: A unit vector is created from another one by dividing the last by its magnitude: We can find a vector of magnitude 2 and opposite to B by multiplying a unit vector parallel to B by -2: The post Vector problems with solution appeared first on YouPhysics