Find the Cartesian equation of the following | vedclass

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(A) The given equation of the plane in vector form is:$\vec{r} \cdot [(s-2t) \hat{i} + (3-t) \hat{j} + (2s+t) \hat{k}] = 15$  ...........$(1)$For any

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$(s-2t)x + (3-t)y + (2s+t)z = 15$

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(A) The given equation of the plane in vector form is:$\vec{r} \cdot [(s-2t) \hat{i} + (3-t) \hat{j} + (2s+t) \hat{k}] = 15$  ...........$(1)$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:$(x \hat{i} + y \hat{j} + z \hat{k}) \cdot [(s-2t) \hat{i} + (3-t) \hat{j} + (2s+t) \hat{k}] = 15$Taking the dot product of the two vectors,we obtain:$(s-2t)x + (3-t)y + (2s+t)z = 15$This is the required Cartesian equation of the plane.

Find the Cartesian equation of the following plane:
$\vec{r} \cdot [(s-2t) \hat{i} + (3-t) \hat{j} + (2s+t) \hat{k}] = 15$

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Find the Cartesian equation of the following plane:$\vec{r} \cdot [(s-2t) \hat{i} + (3-t) \hat{j} + (2s+t) \hat{k}] = 15$