Neco 2023 Further Mathematics Question 19

Practice objective / multiple choice question 19 from the 2023 Neco Further Mathematics examination.

Neco 2023 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 19 NECO • 2023 • FURTHER_MATHEMATICS • objective

Vectors \(\mathbf{a}= (2,-1,3)\) and \(\mathbf{b}= (k,4,-2)\) are such that the angle between them is \(60^{\circ}\). (i) Find the value of \(k\). (ii) Find a vector \(\mathbf{c}\) that is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\) and has magnitude \(5\). Give \(\mathbf{c}\) in component form, rounded to two decimal places.

Answer Options

A. k = 40 + 2\\sqrt{385} \\approx 79.24; c \\approx (3.40, -2.14, -2.98)
B. k = 40 - 2\\sqrt{400} \\approx 0; c \\approx (-3.00, 2.00, 3.00)
Correct Answer C. k = 40 - 2\sqrt{385} \approx 0.76; c \approx (-3.40, 2.14, 2.98)
D. k = 20 - \\sqrt{385} \\approx -0.62; c \\approx (-2.50, 1.80, 2.10)
Correct Answer
C
Correct Option:
k = 40 - 2\sqrt{385} \approx 0.76; c \approx (-3.40, 2.14, 2.98)

About This Question

This is Neco 2023 Further Mathematics Question 19. It is one of the objective questions from the 2023 Neco Further Mathematics examination.

Difficulty level: Hard .

View More Neco 2023 Further Mathematics Questions More Neco Practice Questions Back to Questions

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Chat with Support