Find the coordinates of a unit vector that is perpendicular to both of the vectorsx=(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?

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

Approved