QCEVault

Vectors and matrices — Question 10

QCAA 2022, Paper 1 · 1 mark

Q10 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 10

A plane is represented by the equation x−2z=5x-2z=5. A vector normal to this plane is
(A)
(1−25)\begin{pmatrix}1\\-2\\5\end{pmatrix}
(B)
(102)\begin{pmatrix}1\\0\\2\end{pmatrix}
(C)
(10−2)\begin{pmatrix}1\\0\\-2\end{pmatrix}
(D)
(1−2−5)\begin{pmatrix}1\\-2\\-5\end{pmatrix}
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