cmi-entrance 2017 QB2

cmi-entrance · India · ugmath 15 marks Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines

Let $L$ be the line of intersection of the planes $x + y = 0$ and $y + z = 0$.
(a) Write the vector equation of $L$, i.e., find $(a, b, c)$ and $(p, q, r)$ such that $$L = \{(a, b, c) + \lambda(p, q, r) \mid \lambda \text{ is a real number.}\}$$ (b) Find the equation of a plane obtained by rotating $x + y = 0$ about $L$ by $45^\circ$.

Let $L$ be the line of intersection of the planes $x + y = 0$ and $y + z = 0$.\\
(a) Write the vector equation of $L$, i.e., find $(a, b, c)$ and $(p, q, r)$ such that
$$L = \{(a, b, c) + \lambda(p, q, r) \mid \lambda \text{ is a real number.}\}$$
(b) Find the equation of a plane obtained by rotating $x + y = 0$ about $L$ by $45^\circ$.

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