Question

The direction of a vector V(Xv,Yv,Zv) intersects a sphere on point “B”. Assuming O(0,0,0) as the centre and ‘r’ as the radius of the sphere. The mirror of the vector based on OB direction passes the point C(0,0,h). The “B” coordination, B(Xb,Yb,Zb), is required based on the above parameters.

Answer 1

Answer on Question #70271 – Math – Analytic Geometry

Question

1. The direction of a vector $V(X_V, Y_V, Z_V)$ intersects a sphere on point “$B$”. Assuming $O(0,0,0)$ as the center and ‘$r$’ as the radius of the sphere. The mirror of the vector based on $OB$ direction passes the point $C(0,0,h)$. The “$B$” coordinate, $B(X_B, Y_B, Z_B)$, is required based on the above parameters.

Solution

Vector $V$ is collinear to the vector $OB$ by the definition of a vector. The mirror image of a vector is considered in relation to the same direction. Since the mirror contains a point $C(0,0,h)$, the collinear direction of $OB$ is $OC$, then the vector $V$ and its mirror belong to the $Z$-axis.

Therefore, the point of sphere $B$ belongs to the $Z$-axis, and its coordinates are $(0,0,r)$ or $(0,0,-r)$.

Answer: $B(0,0,-r)$ or $B(0,0,r)$.

Answer provided by https://www.AssignmentExpert.com