If the equation of the plane containing the line \(x+2 y+\) \(3 z-4=0=2 x+y-z+5\) and perpendicular to the plane \(\vec{r}=(\hat{i}-\hat{j})+\lambda(\hat{i}+\hat{j}+\hat{k})+\mu(\hat{i}-2 \hat{j}+3 \hat{k})\) is \(a x+b y+c z\) \(=4\), then \((a-b+c)\) is equal to

[JEE Main 2023, 8 Apr (Shift 1)]

Question

If the equation of the plane containing the line \(x+2 y+\) \(3 z-4=0=2 x+y-z+5\) and perpendicular to the plane \(\vec{r}=(\hat{i}-\hat{j})+\lambda(\hat{i}+\hat{j}+\hat{k})+\mu(\hat{i}-2 \hat{j}+3 \hat{k})\) is \(a x+b y+c z\) \(=4\), then \((a-b+c)\) is equal to

[JEE Main 2023, 8 Apr (Shift 1)]

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If the equation of the plane containing the line \(x+2 y+\) \(3 z-4=0=2 x+y-z+5\) and perpendicular to the plane \(\vec{…

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