Gce Model Questions Vol1 2019 Further Mathematics Question 32

Practice objective / multiple choice question 32 from the 2019 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2019 Further Mathematics Objective / Multiple Choice Medium Difficulty
Question 32 GCE_MODEL_QUESTIONS_VOL1 • 2019 • FURTHER_MATHEMATICS • objective

Vector \(\mathbf{a}= (2,\,-1,\,3)\) and vector \(\mathbf{b}= (k,\,4,\,-2)\) are such that the angle between them is \(60^{\circ}\). (i) Find the possible value(s) of \(k\). (ii) For each value of \(k\), give a unit vector that is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\).

Answer Options

A. k = 0.75 or k = 79.25. For k = 0.75 a unit normal vector is approximately \((-0.600,\,0.500,\,0.620)\). For k = 79.25 a unit normal vector is approximately \((-0.050,\,0.930,\,0.350)\).
B. k = 1.25 or k = 78.0. For k = 1.25 a unit normal vector is approximately \((-0.650,\,0.450,\,0.610)\). For k = 78.0 a unit normal vector is approximately \((-0.035,\,0.938,\,0.345)\).
C. k = 0.5 or k = 80.0. For k = 0.5 a unit normal vector is approximately \((-0.700,\,0.400,\,0.590)\). For k = 80.0 a unit normal vector is approximately \((-0.040,\,0.945,\,0.330)\).
Correct Answer D. k = 0.75 or k = 79.25. For k = 0.75 a unit normal vector is approximately \((-0.681,\,0.426,\,0.596)\). For k = 79.25 a unit normal vector is approximately \((-0.039,\,0.940,\,0.339)\).
Correct Answer
D
Correct Option:
k = 0.75 or k = 79.25. For k = 0.75 a unit normal vector is approximately \((-0.681,\,0.426,\,0.596)\). For k = 79.25 a unit normal vector is approximately \((-0.039,\,0.940,\,0.339)\).

About This Question

This is Gce Model Questions Vol1 2019 Further Mathematics Question 32. It is one of the objective questions from the 2019 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Medium .

View More Gce Model Questions Vol1 2019 Further Mathematics Questions More Gce Model Questions Vol1 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