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Grade: 12

                        

A vector makes an angle of 45 degree with x and y axes. What is the angle formed by the vector with z axis?

2 years ago

Answers : (1)

kkbisht
90 Points
							
Answer is 90 degree. See how?
you know that direction that direction cosines of a vector, say r are nothing but cosines of the anges made by the vector with the three coordinate axes i.e. X-axis , Y-axis, Z-axis with basic  the property that cos2 A + cos2 B + cos2C=1
where A, B, C are the respective angles made by the vector with the axes
You say that the vector makes anles 45 degree with X and Y axis therefore cos245 + cos2 45 +cos2C=1
This implies that (1/\sqrt{}2)2  + (1/\sqrt{}2)22 +cos2C=1 or ½  + ½  + cos2C=1 => cos2C=0 => cos C=0 => C=\pi/2
so anglw made by the vector is \pi/2 with Z-axis
 
kkbisht
2 years ago
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