CUET Mathematics 2023 30 May Shift 3 PYQs

Which of the following statements is/are true?

(A) The vector sum of the three sides of a triangle in order is $\vec{0}$

(B) The magnitude $(r)$, direction ratios $(a, b, c)$ and direction cosines $(l, m, n)$ of any vector $\vec{r} = a\hat{i} + b\hat{j} + c\hat{k}$ are related as $l = \frac{a}{r}, m = \frac{b}{r}, n = \frac{c}{r}$

(C) If θ is the angle between two vectors $\vec{a}$ and $\vec{b}$, then their cross product is given as $\vec{a} \times \vec{b} = |\vec{a}||\vec{b}|\sin \theta$

(D) The cross product of two vectors is commutative

Choose the correct answer from the options given below:

If $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$, where $\vec{a}$ and $\vec{b}$ are unit vectors and $|\vec{c}|=2$, then the angle between the vectors $\vec{b}$ and $\vec{c}$ is :

If $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, $|\vec{a}| = 7$, $|\vec{b}| = 3$ and $|\vec{c}| = 5$, then angle between $\vec{b}$ and $\vec{c}$ is