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:

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