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Find the coordinates of a unit vector that is perpendicular to both of the vectors x=(1,1,1) and y=(1,3,-1) and makes an obtuse angle with the z-axis. and what is the effect of obtuse angle?

Find the coordinates of a unit vector that is perpendicular to both of the vectors

x=(1,1,1) and y=(1,3,-1) and makes an obtuse angle with the z-axis.


and what is the effect of obtuse angle?

Grade:

1 Answers

vikas askiitian expert
509 Points
10 years ago

for  obtice angle , direction cosine should be -ve ...

X = i + j + k

Y = i + 3j - k

here we have two possible vectors which are perpendicular to X & Y ..

P(vector perpendicular to both X & Y) = XxY       or     YxX                       (x represents cross product)

P = -4i + 2j + 2k            or     4i - 2j - 2k

        I                                     II

required solution is II coz it is making an obtuce angle with z axis coz direct cosine is -ve ..

P = 4i - 2j - 2k

P(unit vector) = (4i - 2j -2k)/modP = (4i - 2j - 2k)/root24                 ans

modP = root(16+4+4) = root24

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