Zadanie 7b
For this k, (i) interpret the solutions geometrically; (ii) express them parametrically.
Representing planes
Construct vector and Cartesian equations for planes using points, independent in-plane directions or a normal vector.
Tę umiejętność sprawdza 20 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 20 Otwórz w wyszukiwarce z filtrami
Zadanie 11a
Find a vector equation for the axis through V and the centre of C.
- Materiał graficzny
Zadanie 11e
The housing rotates about the fixed point V so that P moves to P′ = (1, −9, 13). Find an equation of the plane through P, V and P′, with integer coefficients.
Zadanie 11c
The base plane Π is 4x − y + 7z = 18. State a vector equation for its perpendicular L₁ through K.
Zadanie 11a
(i) Show that a=1. (ii) Determine the possible real values of b.
Zadanie 9a
Show that P1 has equation 2x − y + z = 0.
Zadanie 11b
Find a Cartesian equation for Π3.
Zadanie 11d
Find a Cartesian equation of P1.
Zadanie 10f
Let N be the point of L₂ nearest to P. Find a Cartesian equation of the plane through O,P,N.
Zadanie 12b
(i) Give a vector equation of Π. (ii) Given (1, −1, −1) × (2, 1, −1) = (2, −1, 3), show that Π has equation 2x−y+3z=12.
Zadanie 12c
State (i) q; (ii) r.
Zadanie 12e
Give a vector equation of L₃.
Zadanie 12g
Hence find the volume of pyramid PQRS.
Zadanie 11a
Show that A lies on Π₁.
Zadanie 11e
The plane 2x + 4y − z = 25 is at distance from Π₁. Find the other plane Π₃ parallel to Π₁ at the same distance.
Zadanie 11c
Verify that Π contains L.
Zadanie 12d
Find a normal vector to Π.
Zadanie 12e
Find both possible positions of the centre of the cylinder’s other base.
Zadanie 11c
Let L be the line of intersection of Π₁ and Π₂. Find the distance between L and Π₃.
Zadanie 12d
For k≠8, let Π be the plane through A,B,C. (i) Find its Cartesian equation. (ii) Find the point of Π nearest the origin.