Vectors in three dimensions — Question 28
Original QCE Vault practice · 5 marks
Q28 · Practice questionComplex familiar5 marks
QUESTION 28 (5 marks)
Points A(1,0,2), B(3,1,0) and C(0,2,1) lie in a plane. a)Determine a Cartesian equation of the plane.
b)Determine the exact perpendicular distance from D(4,4,7) to the plane. WORKED SOLUTION
Practice marking scheme
5 marksANSWER(a) 3x+4y+5z=13; (b) 52. Worked solution
(a) AB=(2,1,−2) and AC=(−1,2,−1). Their cross product is (3,4,5), a plane normal. Using point A, 3(x−1)+4y+5(z−2)=0⇒3x+4y+5z=13. (b) d=32+42+52∣3(4)+4(4)+5(7)−13∣=5050=52. Determines two direction vectors.
Determines a normal by cross product.
Forms the plane equation.
Calculates the perpendicular distance.
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