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NCERT Class XII Mathematics Chapter - - Solutions

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Question 31 - 33: Find the cartesian equation of the following planes:
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Question : 34 of 78
Marks: +1, -0
r⃗⋅[(s−2t)i^+(3−t)j^+(2s+t)k^]=15\vec{r} \cdot [(s-2t)\hat{i} + (3-t)\hat{j} + (2s+t)\hat{k}] = 15
Solution:  
We have : r⃗⋅[(s−2t)i^+(3−t)j^+(2s+t)k^]=15\vec{r} \cdot [(s-2t)\hat{i} + (3-t)\hat{j} + (2s+t)\hat{k}] = 15
⇒(xi^+yj^+zk^)⋅[(s−2t)i^+(3−t)j^+(2s+t)k^]=15\Rightarrow ( \widehat{xi} + \widehat{yj} + \widehat{zk} ) \cdot [(s-2t)\hat{i} + (3-t)\hat{j} + (2s+t)\hat{k}] = 15
⇒ (s – 2t)x + (3 – t)y + (2s + t) z = 15.
which is the required cartesian equation.
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