1a)Find an equation for the surface consisting of all points P for which the distance from P to the y axis is twice the distance from P to the xz-plane. Identify the surface.
b)Find a vector equation and parametric equations for the line segment that joins P(a; b; c) to Q(u; v; w).
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(a). Let P(x,y,z) be the point in XYZ-plane such that the distance from P to the y axis is twice the distance from P to the xz-plane i.e.
If `d_1=` distance from from P(x,y,z) to y-axis and
`d_2=` distance from P(x,y,z) to xz-plane .
By given condition
Substitute `d_1 and d_2` in (i), we have
(b). Equation of the line in vectors form joining two vectors `vecX_0 and vecX_1` is
`vecX=(1-lambda)vecX_0+lambdavecX_1 , lambda in[0,1]`
Parametric equations are
z=c+lambda(w-c) , lambda in [0,1].
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