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
$\overrightarrow{{}c}=(2 \overrightarrow{{}a} \times \overrightarrow{{}b})-3 \overrightarrow{{}b}$
$\overrightarrow{{}b} \cdot \overrightarrow{{}c}=\overrightarrow{{}b} \cdot(2 \overrightarrow{{}a} \times \overrightarrow{{}b})-3 \overrightarrow{{}b} \cdot \overrightarrow{{}b}$
$=-3|b|^{2}$
$=-48$
