Question

If $\overrightarrow{d}=x\hat{i}+y\hat{j}+z\hat{k}$, then which of the following equations is/are correct?
1. $y-x=4$
2. $2z-3=0$
Select the correct answer using the code given below

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is D Neither 1 nor 2

$\overrightarrow{c}$ is parallel to $\overrightarrow{c}$

$\therefore \overrightarrow{c}=k\overrightarrow{a}$

$\therefore \overrightarrow{c}=k\hat{i}+k\hat{j}$

$\overrightarrow{b}=\overrightarrow{c}+\overrightarrow{d}$

$\therefore 3\hat{i}+4\hat{k}=k\hat{i}+k\hat{j}+x\hat{i}+y\hat{j}+z\hat{k}$

$\therefore 3\hat{i}+4\hat{k}=(k+x)\hat{i}+(k+y)\hat{j}+z\hat{k}$

$\therefore k+x=3$ ...(1)

$k+y=0$ ...(2)

$z=4$ ...(3)

From (2) $k=-y$

Substituting this in equation (1),

$-y+x=3$

$\therefore y-x=-3$

So, the answer is option (D)