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Find the angle between the planes vec r...

Find the angle between the planes ` vec rdot(2 hat i- hat j+ hat k)=6a n d vec rdot( hat i+ hat j+2 hat k)=5.`

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To find the angle between the two planes given by the equations \( \vec{r} \cdot (2\hat{i} - \hat{j} + \hat{k}) = 6 \) and \( \vec{r} \cdot (\hat{i} + \hat{j} + 2\hat{k}) = 5 \), we can follow these steps: ### Step 1: Identify the normal vectors of the planes The normal vector of the first plane \( \vec{n_1} \) can be extracted from the coefficients of the first equation: \[ \vec{n_1} = 2\hat{i} - \hat{j} + \hat{k} \] ...
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Find the equation of the plane passing through the intersection of the planes vec rdot( (hat i+ hat j+ hat k)=1\ a n d\ vec rdot((2 hat i+3 hat j- hat k)+4=0 and parallel to x-axis.

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RD SHARMA-THE PLANE -Solved Examples And Exercises
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  2. Find the vector equation of the plane passing through the points 3 hat...

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  3. Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a ...

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  4. Find the vector equation of the plane passing through the points (1,1,...

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  5. Find the vector equation of the plane passing through the points A(a ,...

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  7. Find the vector equation of a plane which is at a distance of 8 units ...

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  10. Find the equation of a plane which is at a distance of 3sqrt(3) units ...

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  11. Find the equation of the plane passing through the point (-1,2,1) and ...

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  13. Find the equation of the plane passing through the point (1,2,1) and p...

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  15. Find the vector equation of the plane passing through the points havin...

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  16. Find the equation of the plane through the points P(1,\ 1,\ 0),\ Q(1,\...

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