Vectors in problem solving

Vectors in problem solving Quiz

Spec J5 · AQA A-Level Maths: Quiz

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5 questions, one answer each

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1. Forces $(2\mathbf i+3\mathbf j)$ N and $(-4\mathbf i+\mathbf j)$ N act with a third force $\mathbf F$ on a particle in equilibrium. Find $\mathbf F$ .
- A. $(-2\mathbf i+4\mathbf j)$ N
- B. $(2\mathbf i-4\mathbf j)$ N
- C. $(6\mathbf i+2\mathbf j)$ N
- D. $(2\mathbf i+4\mathbf j)$ N
2. $P(1,1)$ , $Q(3,4)$ and $R(7,k)$ are collinear. Find $k$ .
- A. $9$
- B. $12$
- C. $8$
- D. $10$
3. $M$ lies on $AB$ with $AM:MB=2:3$ , and $\overrightarrow{OA}=\mathbf a$ , $\overrightarrow{OB}=\mathbf b$ . Find $\overrightarrow{OM}$ .
- A. $\frac25\mathbf a+\frac35\mathbf b$
- B. $\frac23\mathbf a+\frac13\mathbf b$
- C. $\frac35\mathbf a+\frac25\mathbf b$
- D. $\frac12\mathbf a+\frac12\mathbf b$
4. A $3$ kg particle has a resultant force of $(6\mathbf i-9\mathbf j)$ N. Find its acceleration.
- A. $(2\mathbf i-3\mathbf j)$ m s⁻²
- B. $(18\mathbf i-27\mathbf j)$ m s⁻²
- C. $(6\mathbf i-9\mathbf j)$ m s⁻²
- D. $(3\mathbf i-\frac92\mathbf j)$ m s⁻²
5. Which condition lets you equate coefficients in $p\mathbf a+q\mathbf b=r\mathbf a+s\mathbf b$ ?
- A. $\mathbf a$ and $\mathbf b$ are parallel
- B. $\mathbf a$ and $\mathbf b$ are equal in length
- C. $\mathbf a$ and $\mathbf b$ are not parallel
- D. $p$ and $q$ are positive