Mathematics In Physics Question 1
Question 1 - 24 January - Shift 1
Vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other when $3 a+2 b=7$, the ratio of a to $b$ is $\frac{x}{2}$. The value of $x$ is
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Answer: (1)
Solution:
For two perpendicular vectors
$ \begin{aligned} & (a \hat{i}+b \hat{j}+\hat{k}) \cdot(2 \hat{i}-3 \hat{j}+4 \hat{k})=0 \\ & 2 a-3 b+4=0 \end{aligned} $
On solving, $2 a-3 b=-4$
Also given
$ 3 a+2 b=7 $
We get $a=1, b=2$
$ \frac{a}{b}=\frac{x}{2} \Rightarrow x=\frac{2 a}{b}=\frac{2 \times 1}{2} $
$\Rightarrow x=1$
