waec model questions vol6 2024 mathematics
Objective • Question 19
Question 19
WAEC_MODEL_QUESTIONS_VOL6
•
2024
In three‑dimensional space, vectors \(\mathbf{a}\) and \(\mathbf{b}\) have magnitudes |\(\mathbf{a}\)| = 3 cm and |\(\mathbf{b}\)| = 4 cm, and the angle between them is 60°. Define \(\mathbf{d} = \mathbf{a} + k\mathbf{b}\) where the scalar k is chosen so that \(\mathbf{d}\) is perpendicular to \(\mathbf{a} - 2\mathbf{b}\). Determine the value of k and then give the magnitude of \(\mathbf{d}\) in simplest radical form.
Answer Options
A.
k = 3\/26, |d| = 21√3\/13 cm
Correct Answer
B.
k = -3/26, |d| = 21√3/13 cm
C.
k = -3\/26, |d| = 14√3\/13 cm
D.
k = -1\/2, |d| = 7√3\/2 cm
Correct Answer
B
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