QCEVault

Vectors and matrices — Question 6

QCAA 2022, Paper 1 · 1 mark

Q6 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 6

The Cartesian equation for a sphere with centre (−2,3,−4)(-2,3,-4) and radius 99 is
(A)
(x−2)2+(y+3)2+(z−4)2=9(x-2)^2+(y+3)^2+(z-4)^2=9
(B)
(x+2)2+(y−3)2+(z+4)2=9(x+2)^2+(y-3)^2+(z+4)^2=9
(C)
(x−2)2+(y+3)2+(z−4)2=81(x-2)^2+(y+3)^2+(z-4)^2=81
(D)
(x+2)2+(y−3)2+(z+4)2=81(x+2)^2+(y-3)^2+(z+4)^2=81
Question linkOriginal paper

Related questions

  1. Q2 · 2025 QCAA · Paper 1 · 1 mark
    The position vector of a particle at time tt is given by r=sin⁡(t)i^+cos⁡(t)j^\mathbf r=\sin(t)\hat{\mathbf i}+\cos(t)\hat{\mathbf j}. The path of the particle is
    Vectors and matrices
  2. Q6 · 2025 QCAA · Paper 1 · 1 mark
    At time tt, a particle travels with a velocity of v=(21+t2)i^−2tj^\mathbf v=\left(\dfrac{2}{1+t^2}\right)\hat{\mathbf i}-2t\hat{\mathbf j}. Determine a general expression for the position vector, r\mathbf r, of the particle during this motion.
    Vectors and matrices
  3. Q8 · 2025 QCAA · Paper 1 · 1 mark
    The position vectors of two objects over time, tt, where t≥0t\ge0, are given by r1(t)=−2i^+t2j^\mathbf r_1(t)=-2\hat{\mathbf i}+t^2\hat{\mathbf j} and r2(t)=ati^+4j^\mathbf r_2(t)=at\hat{\mathbf i}+4\hat{\mathbf j} (where a∈Ra\in\mathbb R). Given that the two objects collide, the value of aa is
    Vectors and matrices
  4. Q11 · 2025 QCAA · Paper 1 · 5 marks
    Consider the system of linear equations represented using the augmented matrix shown. [1−1−1−6−21110044]\left[\begin{array}{ccc|c}1&-1&-1&-6\\-2&1&1&1\\0&0&4&4\end{array}\right] Key: R1R_1 represents the row 1 values.
    Vectors and matrices