Skip to content

Course home

1.13 J: Vectors

1.13 J: Vectors

EasyMediumHard
12345678910111213141516171819202122232425
Question 23

The point A A\,A has position vector

a=5i−3j+4k\mathbf{a} = 5\mathbf{i} - 3\mathbf{j} + 4\mathbf{k}a=5i−3j+4k

The point P P\,P has position vector p=λi+2j+k\mathbf{p} = \lambda\mathbf{i} + 2\mathbf{j} + \mathbf{k}p=λi+2j+k, where λ \lambda\,λ is a constant.

a.

Show that ∣AP⃗∣2=λ2−10λ+59\left|\vec{AP}\right|^2 = \lambda^2 - 10\lambda + 59​AP​2=λ2−10λ+59.

[3]
b.

Find the value of λ \lambda\,λ for which ∣AP⃗∣\left|\vec{AP}\right|​AP​ is least, and state that least value in exact form.

[3]
c.

Find the set of values of λ \lambda\,λ for which ∣AP⃗∣>7\left|\vec{AP}\right| > 7​AP​>7.

[2]
Markscheme

1.13 J: Vectors Questions

  1. A Level
  2. /Maths
  3. /1.13 J: Vectors

168 exam-style questions on AQA A Level Maths 1.13 J: Vectors, covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank