# Dot product problems with solution

Problem statement:

Given the vectors: A = 3i + 2jk and B = 5i +5j, find:

1. The dot product AB.
2. The projection of A onto B.
3. The angle between A and B.
4. A vector of magnitude 2 in the XY plane perpendicular to B. Knowledge is free, but servers are not. Please consider supporting us by disabling your ad blocker on YouPhysics. Thanks!

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.

The dot product of two vectors A and B expressed in unit vector notation is given by: Remember that the dot product returns a scalar (a number). Knowledge is free, but servers are not. Please consider supporting us by disabling your ad blocker on YouPhysics. Thanks!

To find the projection of A onto B we divide the dot product we have determined before by the magnitude of B (visit the page dot product for more information): The angle between both vectors is given by the expression we derived when we defined the dot product: In order to find a vector C perpendicular B we equal their dot product to zero.

Vector C written in unit vector notation is given by: And the dot product is: The previous equation is the first condition that the components of C must obey. Moreover, its magnitude has to be 2: And substituting the condition given by the dot product: Finally, C expressed in unit vector notation is given by: The post Dot product problems with solution appeared first on YouPhysics