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Find the equation of the plane containing the lines `(x-5)/4=(y-7)/4=(z+3)/(-5)a n d(x-8)/7=(y-4)/1=(z-5)/3dot`

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To find the equation of the plane containing the two given lines, we can follow these steps: ### Step 1: Identify the direction ratios of the lines The first line is given by the equation: \[ \frac{x-5}{4} = \frac{y-7}{4} = \frac{z+3}{-5} ...
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Show that the lines (x-5)/4=(y-7)/4=(z+3)/(-5) and (x-8)/7=(y-4)/1=(z-5)/3 intersect each other

Find the equation of the plane containing the line (x+1)/3=(y-3)/5=(z+2)/(-2) and the point (0,7,-7) and show that the line x/1=(y-7)/(-3)=(z+7)/2 also lies in the same plane.

The equation of the plane which is equally inclined to the lines (x-1)/2=y/(-2)=(z+2)/(-1)a n d=(x+3)/8=(y-4)/1=z/(-4) and passing through the origin is/are a. 14 x-5y-7z=0 b. 2x+7y-z=0 c. 3x-4y-z=0 d. x+2y-5z=0

The equation of the plane which is equally inclined to the lines (x-1)/2=y/(-2)=(z+2)/(-1)a n d=(x+3)/8=(y-4)/1=z/(-4) and passing through the origin is/are a. 14 x-5y-7z=0 b. 2x+7y-z=0 c. 3x-4y-z=0 d. x+2y-5z=0

Find the equation of the plane passing through the line (x-1)/5=(y+2)/6=(z-3)/4 and point (4,3,7)dot

The perpendicular distance from the origin to the plane containing the two lines, (x+2)/3=(y-2)/5=(z+5)/7 and (x-1)/1=(y-4)/4=(z+4)/7 is: (a) 11sqrt6 (b) 11/(sqrt6) (c) 11 (d) 6sqrt(11)

If the distance between the plane ax 2y + z = d and the plane containing the lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)/3=(y-3)/4=(z-4)/5 is sqrt6 , then value of |d| is

Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/4a n d(x-2)/3=(y-4)/4=(z-5)/5 .

Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/4a n d(x-2)/3=(y-4)/4=(z-5)/5 .

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CENGAGE ENGLISH-THREE-DIMENSIONAL GEOMETRY -CONCEPT APPLICATION EXERCISE 3.3
  1. Find the angle between the line (x-1)/3=(y-1)/2=(z-1)/4 and the pla...

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  2. Find the distance between the line (x+1)/(-3)=(y-3)/2=(z-2)/1 and t...

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  3. Find the distance of the point (-1,-5,-10) from the point of int...

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  4. Find the equation of the plane passing through the point ( 1, 3, 2)an...

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  5. Find the equation of the plane passing through the points (1,0,-1)a...

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  6. Find the equation of the plane containing the lines (x-5)/4=(y-7)/4...

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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 plane perpendicular to the line (x-1)/2=(y...

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

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  10. Find the angle between the line vecr=hati+2hatj-hatk+lamda(hati-hatj+h...

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  11. Find the equation of the plane which passes through the point (12,3...

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

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  13. Find the equation of a plane which is parallel to the plane x-2y+2z...

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

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  15. Find the equation of the image of the plane x-2y+2z=3 in the plane x+y...

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  16. Find the equation of the plane through the points (23,1)a n d(4,-5,...

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  17. Find the distance of the point veca from the plane vecr*hatn=d measure...

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

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

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