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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

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=1where A, B, C are the respective angles made by the vector with the axesYou say that the vector makes anles 45 degree with X and Y axis therefore cos245 + cos2 45 +cos2C=1This implies that (1/$\sqrt{}$2)2  + (1/$\sqrt{}$2)22 +cos2C=1 or ½  + ½  + cos2C=1 => cos2C=0 => cos C=0 => C=$\pi$/2so anglw made by the vector is $\pi$/2 with Z-axis kkbisht

2 years ago
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