QCEVault

Vectors and matrices — Question 8

QCAA 2025, Paper 2 · 1 mark

Q8 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 8

Consider the plane that contains both the xx-axis and the yy-axis. A sphere centred at (3,4,6)(3,4,6) touches this plane.
The length of the radius of the sphere is
(A)
33 units.
(B)
44 units.
(C)
55 units.
(D)
66 units.
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