# 2022 EJC J2 MYE P1 Q2

## Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.
##### 2022 EJC J2 MYE P1 Q2

Vectors $\mathbf{a}$,$\mathbf{b}$ and $\mathbf{c}$ are such that $\mathbf{a}\ne \mathbf{0}$, $2\mathbf{b}\ne 3\mathbf{c}$, and $2\mathbf{a}\mathbf{.b}=3\mathbf{a}\mathbf{.c}$.

(a)

Show that $\mathbf{a}$ is perpendicular to $2\mathbf{b}-3\mathbf{c}$.

[2]

(b)

It is now given that $\mathbf{b}$ is a unit vector, that the modulus of $\mathbf{c}$ is $\frac{4}{3}$ and that $\mathbf{a}$ is parallel to $\mathbf{b}$. Find the angle between $\mathbf{b}$ and $\mathbf{c}$.

[3]

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Published: 22nd February 2024
Written by
Timothy Gan
This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.
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