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Find the equation of the plane which passes through the point `(1,2,3)` and which is at the minimum distance from the point `(-1,0,2)dot`

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To find the equation of the plane that passes through the point \( (1, 2, 3) \) and is at the minimum distance from the point \( (-1, 0, 2) \), we can follow these steps: ### Step 1: Identify the Points Let point \( A \) be \( (1, 2, 3) \) (the point through which the plane passes) and point \( B \) be \( (-1, 0, 2) \) (the point from which we want to minimize the distance to the plane). ### Step 2: Find the Direction Vector We need to find the vector \( \overrightarrow{AB} \) which is the vector from point \( A \) to point \( B \). This can be calculated as: \[ ...
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CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Find the equation of a plane which is parallel to the plane x-2y+2z=5 ...

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  2. Find the direction ratios of orthogonal projection of line (x-1)/(1)=(...

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  3. Find the equation of the plane which passes through the point (1,2,...

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  4. Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+la...

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  5. Find the equation of the plane passing through the line (x-1)/(5)=(y+2...

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  6. Find the equation of the plane perpendicular to the line (x-1)/2=(y...

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  7. Find the equation of the plane passing through the straight line (x...

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  8. Find the equation of the line drawn through the point (1, 0,2) to meet...

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  9. If vecr=(hati+2hatj+3hatk)+lambda(hati-hatj+hatk) and vecr=(hati+2hatj...

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  10. Find the coordinates of a point on the (x-1)/2=(y+1)/(-3)=z atg a d...

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  11. Line L1 is parallel to vector vecalpha=-3 hat i+2 hat j+4 hat k and p...

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  12. Find the values p so that line (1-x)/3=(7y-14)/(2p)=(z-3)/2a n d(7-7x)...

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  13. Find the angel between the following pair of lines: vec r=2 hat i...

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  14. Fid the condition if lines x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime)...

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  15. Find the acute angle between the lines (x-1)/l=(y+1)/m=1/na n d=(x+...

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  16. Find the length of the perpendicular drawn from point (2,3,4) to li...

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  17. Find the coordinates of the foot of the perpendicular drawn from po...

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  18. Find the vector equation of the line passing through (1,2,3) and pa...

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  19. Find the value of m for which thestraight line 3x-2y+z+3=0=4x+3y+4z+1...

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  20. Show that the lines (x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alph...

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