ACSEE (Form 6) Vectors — practice questions

Explore 3 free Vectors questions in ACSEE (Form 6) Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vectors questions and exercises with answers

Showing questions 1–3 of 3.

Forces $2i-5j+6k$ and $-i-2j-k$ move a particle from $A(4,-3,-2)$ to $B(6,-1,-3)$. The work done is:Read the answer and worked solution →Vector $PQ$ has magnitude 5 units and is inclined at $150^{\circ}$ to the $x$-axis. In the form $ai+bj$ it is:Read the answer and worked solution →Vectors, true or falseRead the answer and worked solution →

Worked practice questions

Forces $2i-5j+6k$ and $-i-2j-k$ move a particle from $A(4,-3,-2)$ to $B(6,-1,-3)$. The work done is:

66 units
33 units
17 units
11 units

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Correct answer: C. 17 units

1. Work done is $W=\vec{F}\cdot\vec{AB}$, so first find the resultant force. 2. $\vec{F}=(2i-5j+6k)+(-i-2j-k)=i-7j+5k$. 3. The displacement is $\vec{AB}=(6-4)i+(-1+3)j+(-3+2)k=2i+2j-k$. 4. Dot product: $(1)(2)+(-7)(2)+(5)(-1)=2-14-5=-17$. 5. Taking the magnitude, the work done is $17$ units. The value $66$ comes from doubling a mis-formed dot product rather than summing the forces first. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 3: Vectors_

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Vector $PQ$ has magnitude 5 units and is inclined at $150^{\circ}$ to the $x$-axis. In the form $ai+bj$ it is:

$-\frac{5\sqrt3}{2}i+\frac{5}{2}j$
$-\frac{5}{2}i+\frac{5\sqrt3}{2}j$
$\frac{5\sqrt3}{2}i+\frac{5}{2}j$
$-\frac{5\sqrt3}{2}i-\frac{5}{2}j$

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Correct answer: A. $-\frac{5\sqrt3}{2}i+\frac{5}{2}j$

1. Resolve into components: $a=|PQ|\cos\theta$ and $b=|PQ|\sin\theta$. 2. $\cos 150^{\circ}=-\dfrac{\sqrt3}{2}$, so $a=5\times\left(-\dfrac{\sqrt3}{2}\right)=-\dfrac{5\sqrt3}{2}$. 3. $\sin 150^{\circ}=\dfrac12$, so $b=5\times\dfrac12=\dfrac52$. 4. Hence $\vec{PQ}=-\dfrac{5\sqrt3}{2}i+\dfrac{5}{2}j$. 5. At $150^{\circ}$ the vector lies in the second quadrant, so $a$ must be negative and $b$ positive; any option breaking that sign pattern is wrong. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 3: Vectors_

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Vectors, true or false

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Questions

Statement is true
Yes
Statement
A zero dot product means the vectors are perpendicular
Statement is true
Yes
Statement
Work done is the dot product of force and displacement
Statement is true
Yes
Statement
The resultant of two forces is found by adding components
Statement is true
No
Statement
cos 150° is positive
Statement is true
Yes
Statement
A triangle with sides √41, √35 and √6 is right-angled

Instructions

Swipe true or false for each claim.

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