Find the Cartesian equation of the following | vedclass

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(A) The given equation of the plane in vector form is $\vec{r} \cdot (2\hat{i} + 3\hat{j} - 4\hat{k}) = 1$  ..........$(1)$For any arbitrary point $P(

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$2x + 3y - 4z = 1$

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(A) The given equation of the plane in vector form is $\vec{r} \cdot (2\hat{i} + 3\hat{j} - 4\hat{k}) = 1$  ..........$(1)$For any arbitrary point $P(x, y, z)$ on the plane,the position vector $\vec{r}$ is given by $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$.Substituting the value of $\vec{r}$ in equation $(1)$,we get:$(x\hat{i} + y\hat{j} + z\hat{k}) \cdot (2\hat{i} + 3\hat{j} - 4\hat{k}) = 1$Taking the dot product of the two vectors,we obtain:$2x + 3y - 4z = 1$This is the required Cartesian equation of the plane.

Find the Cartesian equation of the following plane: $\vec{r} \cdot (2\hat{i} + 3\hat{j} - 4\hat{k}) = 1$

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