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Write a vector normal to the plane vec ...

Write a vector normal to the plane ` vec r=l vec b+m vec c`

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Find the normal of a given plane
Since the plane passes through vector `bar{b}` and `bar{c}`
The normal of the plane is also normal of vector `bar{b}` and `bar{c}`.
The normal vector of `bar{b}` and `bar{c}` is `bar{b} times bar{c}`
The vector normal of the plane is according to formula (1)
`vec{n}=bar{b} times bar{c}`
The final answer is `bar{b} times bar{c}`.
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Write the plane vec rdot((2 hat i+3 hat j-6 hat k)=14 in normal form.

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  2. Write the equation of the plane vec r= vec a+lambda vec b+mu vec c\ ...

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  3. Write a vector normal to the plane vec r=l vec b+m vec c

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  4. Write the equation of the plane passing through (2, -1,1) and parallel...

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  5. Write the equation of the plane containing the lines vec r= vec a+lam...

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  6. Write the position vector of the point where the line vec r= vec a+la...

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  7. Write the value of k for which the line (x-1)/2=(y-1)/3=(z-1)/(k) is p...

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  8. Write the intercept cut off by the plane 2x+y-z=5 on x-axis.

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  9. Find the length of the perpendicular drawn from the origin to the p...

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  10. Write the vector equation of the line passing through the point (1, -2...

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  11. Write the vector equation of the plane passing through the point (a, b...

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  12. The acute angle between the planes 2x-y+z=6\ a n d\ x+y+2z=3 is 45^0\ ...

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  13. The equation of the plane thrugh the ointersection of lane x+2y+3z=4 a...

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  14. The distance between the planes 2x+2y-z+ 2=0\ a n d\ 4x+4y-2z+5=0 is a...

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  15. The image of the point (1, 3, 4) in the plane 2x-y+z+3=0 is (3,\ 5,\ 2...

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  16. Find the vector equation of the following plane in scalar product form...

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  17. The distance of the line vec r=2 hat i-2 hat j+3 hat k+lambda( hat i-...

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  18. The equation of the plane through the line x+y+z+3=0=2x-y+3z+1 and par...

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  19. The vector equation of the plane containing the line vec r=(-2 hat ...

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  20. A plane meets the coordinate axes at A ,\ B ,\ C such that the centroi...

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