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With respect to a fixed origin O, the lines l_1 and l_2 are given by the equations l_1: r = (-9i + 10j) + λ(2i + j - k) l_2: r = (3i + j + 17k) + μ(3i - j + 5k) where λ and μ are scalar parameters - Edexcel - A-Level Maths Pure - Question 8 - 2008 - Paper 7
Question 8
With respect to a fixed origin O, the lines l_1 and l_2 are given by the equations l_1: r = (-9i + 10j) + λ(2i + j - k) l_2: r = (3i + j + 17k) + μ(3i - j + 5k) ... show full transcript
Worked Solution & Example Answer:With respect to a fixed origin O, the lines l_1 and l_2 are given by the equations l_1: r = (-9i + 10j) + λ(2i + j - k) l_2: r = (3i + j + 17k) + μ(3i - j + 5k) where λ and μ are scalar parameters - Edexcel - A-Level Maths Pure - Question 8 - 2008 - Paper 7
Step 1
Find the position vector of B.
Answer
To find the image point B after reflection in line l_2, we first find the projection of A onto l_2.
Let OA = (5i + 7j + 3k).
First, we find the point of intersection P of line l_2 and the line through A along the direction perpendicular to l_2. \
Using the direction vector of l_2 computed previously and following the reflection formula: \
B = 2P - A,
we can now calculate the exact position vector of B.