Vector Algebra Question 14

Question 14 - 30 January - Shift 2

Let $\vec{a}$ and $\vec{b}$ be two vectors. Let $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$, then the value of $\overrightarrow{{}b} \cdot \overrightarrow{{}c}$ is

(1) -24

(2) -48

(3) -84

(4) -60

Show Answer

Answer: (2)

Solution:

Formula: Properties of Scalar product of vectors, Properties of Cross product of vectors

$\overrightarrow{{}c}=(2 \overrightarrow{{}a} \times \overrightarrow{{}b})-3 \overrightarrow{{}b}$

$\overrightarrow{{}b} \cdot \overrightarrow{{}c}=\overrightarrow{{}b} \cdot(2 \overrightarrow{{}a} \times \overrightarrow{{}b})-3 \overrightarrow{{}b} \cdot \overrightarrow{{}b}$

$=-3|b|^{2}$

$=-48$