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Show that the line through the points `(1, 1, 2), (3, 4, 2)` is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

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To show that the line through the points \( (1, 1, 2) \) and \( (3, 4, 2) \) is perpendicular to the line through the points \( (0, 3, 2) \) and \( (3, 5, 6) \), we will follow these steps: ### Step 1: Find the direction ratios of the first line The direction ratios of a line passing through two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) can be found by subtracting the coordinates of the first point from the second point. For the first line through points \( (1, 1, 2) \) and \( (3, 4, 2) \): - Direction ratios \( L_1 = (3 - 1, 4 - 1, 2 - 2) = (2, 3, 0) \). ...
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Show that the line through the points (1, -1, 2) and (3, 4,-2) is perpendicular to the through the points (0, 3,2) and (3, 5, 6).

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Show that the line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (3,-3) and (5,-9).

Show that the line joining the point A(1,-1,2) and B(3, 4, -2) is perpendicular to the line joining the points C(0,3,2) and D(3,5,6).

Show that the line through the points (-2,6) and (1,7) is perpendicular to the line through the points (3,-3) and (5,-9).

Show that the line through the point (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (-1, -2, 1) and (1, 2, 5).

Find the value of p for which the line through the points A(4,1,2) and B(5,p,0) is perpendicular to the line through the points C(2,1,1) and D(3,3,-1) .

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NCERT-THREE DIMENSIONAL GEOMETRY-EXERCISE 11.2
  1. Show that the three lines with direction cosines (12)/(13),(-3)/(13),...

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  2. Show that the line through the points (4, 7, 8), (2, 3, 4)is parallel...

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  3. Show that the line through the points (1, 1, 2), (3, 4, 2) is perpe...

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  4. Find the equation of the line in vector and in cartesian form that pa...

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

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  6. The cartesian equation of a line is (x-5)/3=(y+4)/7=(z-6)/2. Write i...

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  7. Find the cartesian equation of the line which passes through the poin...

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  8. Find the vector and the cartesian equations of the line that passes t...

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  9. Find the vector and the cartesian equations of the lines that passes ...

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  10. Find the values of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2an...

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  11. Show that the lines (x-5)/7=(y+2)/(-5)=z/1and x/1=y/2=z/3are perpendi...

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  12. Find the angle between the following pairs of lines:(i) vec r=2 hat i...

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  13. Find the angle between the following pair of lines: (i) (x-2)/2=(y-1)...

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  14. Find the shortest distance between the lines whose vector equations a...

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  15. Find the shortest distance between the lines whose vector equations a...

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  16. Find the shortest distance between the lines vec r=( hat i+2 hat j+ ...

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  17. Find the shortest distance between the lines(x+1)/7=(y+1)/(-6)=(z+1)/...

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