EDUCATION FOR BETTER TOMMROW
Saturday, 9 August 2014
CHAPTER 4-Worked Out Examples 2
have direction cosines
respectively. Find the angle at which
are inclined to each other respectively.
The unit vectors
respectively can be written as
) is given by
We can dedude the following conditions on the direction cosines of
What will be the corresponding conditions had a set of direction ratios been specified instead of the direction cosines?
For the lines
of the previous example, find the direction cosines of the line
perpendicular to both
Let the unit vector along
is a unit vector itself, the direction cosines of
Find the angle between the lines whose direction cosines are given by the equations
Using the value of
from the first equation in the second, we have
. A set of direction ratios of one line is therefore
A set of direction ratios of the other line is therefore
Using the result of example
(the one that you were asked to prove at the end of the question), the angle between the two lines can now be evaluated to be
August 09, 2014
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