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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | IB Analysis and Approaches |
(a) Find the equation of the intersection of these two planes:
$$ 3x-y+2z = 5 $$ $$ x+y+3z=15$$(b) Find the shortest distance from this line to the origin.
2. | IB Analysis and Approaches |
Consider the three planes:
$$ \Pi_1: \quad x+3y+2z=5 $$ $$ \Pi_2: \quad 2x+y+9z=20 $$ $$ \Pi_3: \quad x-y+6z=8 $$(a) Show that the three planes do not have a common point of intersection.
(b) Verify that the point \(P(1 , 0 , 2)\) lies on both \( \Pi_1 \text{ and } \Pi_2 \)
(c) Find a vector equation of \(L\), the line of intersection of \( \Pi_1 \text{ and } \Pi_2 \)
(d) Find the distance between \(L\) and \( \Pi_3 \)
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