(c) Find the projection of the line segment joining the points (1, −1, 6) and (4, 3, 2) on the line
To find the projection of the line segment joining the points \( A(1, -1, 6) \) and \( B(4, 3, 2) \) on the given line, we will proceed step-by-step. ### Step 1: Direction ratios of the line segment joining \( A(1, -1, 6) \) and \( B(4, 3, 2) \) The direction ratios of the line joining the points \( A \) and \( B \) are given by the vector: \[ __________ _________ ________ ________ _______ _______ ______ ______ ____ ______.
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(b) Transform the equation by shifting the origin to (1, 2, 0) without changing the directions of the coordinate axes. What object does this new equation represent? Give a rough sketch of it.
(b) Prove that the conic passing through the points of intersection of two rectangular hyperbolas is also a rectangular hyperbola.
(b) Find the equation of the sphere touching the plane at (3, −1, −1) and cutting the sphere
orthogonally.
(b) Find the equation of tangent plane to the conicoid Represent the tangent plane geometrically.
(a) Trace the conic
(a) Identify and trace the conicoid Describe its sections by the planes
(a) Examine which of the following conicoids are central and which are non-central. Also determine which of the central conicoids have centre at the origin.
(i)
(ii)
(iii)