Question

Statement-1 : the two vectors $a=1i+Pj+2k$ and $b=3i+3j+Qk$ are parallel only if $P=1$ and $Q+6$.
Statement-2 : if two vectors $a=a_{1}i+a_{2}j+a_{3}k$ and $b=b_{1}i+b_{2}j+b_{3}k$ are parallel then $\frac{a_1}{a_2}=\frac{b_1}{b_2}$

• A. Both statements are true and Statement-2 is correct explanation of Statement-1
• B. Both statements are true and Statement-2 is not correct explanation of Statement-1
• C. Statement-2 is false but other is true
• D. Statement-1 is false but other is true

Answer 1

The correct option is C Statement-2 is false but other is true

Two vectors $a=a_{1}i+a_{2}j+a_{3}k$ and $b=b_{1}i+b_{2}j+b_{3}k$ are parallel if and only if $\frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{a_3}{b_3}$

$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}$

So second statement is correct

In statement one , the vectors are $a=1i+Pj+2k$ and $b=3i+3j+Qk$ are parallel if and only if $\frac{1}{3}=\frac{P}{3}=\frac{2}{Q}$

$\Rightarrow P=1$ and $Q=6$

So statement one is wrong

Therefore option $C$ is correct