Question

$A$: The angle between $2\hat{i}-m\hat{j}+3m\hat{k}$ and $(1+m)\hat{i}-2m\hat{j}+\hat{k}$ is acute angle for $m$$\notin [-2,-\frac{1}{2}].$

$R:$ If $(a,b)$ is acute , then $a.b>0$

• A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
• B. Both $A$ and $R$ are true and $R$ is not correct explanation of $A$
• C. $A$ is true but $R$ is false
• D. $A$ is false but $R$ is true

Answer 1

The correct option is A Both $A$ and $R$ are true and $R$ is the correct explanation of $A$

The reason is a correct statement.
Applying it for the assertion made, we get $2(1+m)+2m^2+3m>0$
$\Rightarrow 2m^2+5m+2>0$
$\Rightarrow m\notin [-2,-\frac{1}{2}]$
Hence the assertion also is true and hence the correct option is $A$