let ' n ' vector be a vector of magnitude 2√3 such that it makes equal acute angles with the co-ordinate Axes find the vector and cartesian forms of the equation of a plane passing through ( 1, - 1, 2 ) and normal to 'n' vector.
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Magnitude of vector 'n'= 2
It is given that vector makes equal angles with coordinate axes.If l, m, and n are direction cosines of a line then
l=Cos A, m =Cos B, n=Cos C
As it is given that the vector n makes equal angle with coordinate axes,
So, A=B=C
As we know
l²+m²+n²=1
Substituting the value of l, m and n, we get
Cos²A+Cos²A+Cos²A=1
3 Cos²A=1
→Cos A=
So the Vector n is =
Direction ratios of normal is (2,2,2)
Equation of plane passing through (1,-1,2) and normal to vector n having direction cosines (2,2,2) is given by
→2(x-1) +2(y+1)+2(z-2)=0
→x-1+y+1+z-2=0
→x+y+z-2=0
→x+y+z=2
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Answer:
Cartesian form- x+y+z=2
Vector form- (i^+j^+k^).r =2
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