A) \[5i+j+jk\]
B) \[-6i+j+5k\]
C) \[5i-j-5k\]
D) \[5i+j-5k\]
Correct Answer: C
Solution :
Let the required vector be \[a=xi+yj+zk.\]It makes equal angles with the vectors \[b=\frac{1}{3}(i-2j+2k)\] \[c=\frac{1}{5}(-4i-3k),d=j\] \[\therefore \]\[a.b=a.c=a.d\][\[\because \] b, c, d are unit vectors] If \[a.b=a.d,\]then \[\frac{1}{3}(x-2y+2z)=y\] If \[a.c=a.d,\]then \[\frac{1}{5}(-4x-3z)=y\] \[\Rightarrow \] \[x-5y+2z=0\] and \[4x+5y+3z=0\] Solving these equation, we get \[x=-z\]and \[x=-5y\] \[\therefore \] \[\frac{x}{-5}=\frac{y}{1}=\frac{z}{5}\] \[\Rightarrow \] \[\frac{x}{5}=\frac{y}{-1}=\frac{z}{-5}\] \[\therefore \] \[a=-5i+j+5k\] or \[a=5i-j-5k\]You need to login to perform this action.
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