Using vector algebra and the position vector R locates an arbitrary point in space), answer the two items below:
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Question

Using vector algebra and the position vector R locates an arbitrary point in space), answer the two items

below:

a)Find the coordinate-independent equation of a plane with unit normal n_hat, whose closest distance to the origin is equal to p. Assume that the unit normal n_hat points away from ), and that an arbitrary point on the plane is located by vector R.

b) Assuming that n_hat = x_hat n1 + y_hat n2 + z_hat n3, provide the cartesian equation of the plane in (a)

NOTE : n_hat, x_hat, y_hat, z_hat are the unit vectors in n,x,y,z direction respectively

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