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Show that the points whose position vectors are `-2 hat i+3 hat j ,\ hat i+2 hat j+3 hat k\ a n d\ 7 hat i+9 hat k` e collinear.

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Show that the points whose position vectors are 5 hat i+5 hat k ,\ 2 hat i+ hat j+3 hat k\ a n d-4 hat i+3 hat j- hat k are collinear.

Prove that the points having position vectors hat i+2 hat j+3 hat k ,\ 3 hat i+4 hat j+7 hat k ,\ -3 hat i-2 hat j-5 hat k are collinear.

Show that four points whose position vectors are 6 hat i-7 hat j ,\ 16 i-19 hat j-4 hat k ,\ 3 hat i-6 hat k ,\ 2 hat i-5 hat j+10\ hat k are coplanar.

Show that the points A, B, C with position vectors 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the triangle.

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i- hat k) are collinear.

Show that the points whose position vectors are as given below are collinear: 2 hat i+ hat j- hat k ,\ 3 hat i-2 hat j+ hat k\ a n d\ hat i+4 hat j-3 hat k 3 hat i-2 hat j+4 hat k ,\ hat i+ hat j+ hat k\ a n d-\ hat i+4 hat j-2 hat k

Show that the points having position vectors 6 hat i-7 hat j ,\ 16 hat i-19 hat j-4 hat k ,\ 3 hat j-6 hat k ,\ 2 hat i+5 hat j+10 hat k are not coplanar.

The four points whose position vector are 6 hat i - 7 hat j,16 hat i - 29 hat j - 4 hat k, 3 hat j - 6 hat k, 2 hat i + 5 hat j + 10 hat k are coplanar

Show that the four points having position vectors 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k ,2 hat i-5 hat j+10 hat k are coplanar.

If three points A ,\ B ,\ a n d\ C have position vectors hat i+x hat j+3 hat k ,\ 3 hat i+4 hat j+7 hat k\ a n d\ y hat i-2 hat j-5 hat k respectively are collinear, them (x , y)= a. (2,-3) b. (-2,3) c. (-2,-3) d. (2,3)

RD SHARMA ENGLISH-STRAIGHT LINE IN SPACE -All Questions
  1. Find the direction cosines of the line (4-x)/2=y/6=(1-z)/3dot Also, re...

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  2. Find the points on the line (x+2)/3=(y+1)/2=(z-3)/2\ at a distance ...

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  3. Show that the points whose position vectors are -2 hat i+3 hat j ,\ h...

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  4. Find the Cartesian and vector equations of a line which passes through...

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  5. The Cartesian equations of a line are 3x+1=6y-2=1-z , find the fixed p...

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  6. Prove that the line x=a y+b ,\ z=c y+d\ a n d\ x=a^(prime)y+b^(prime),...

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  7. Find the equation of a line passing through a point (2, -1, 3) and p...

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  8. Find the Cartesian equations of the line passing through the point (-1...

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  9. The line through hat i+3 hat j+2 hat k and | to the line vec r=( hat...

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  10. Show that the three lines with direction cosines (12)/(13),(-3)/(13),(...

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  11. Show that the line through the points (1, -1, 2) and (3, 4,-2) is p...

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  12. Show that the line through the point (4, 7, 8) and (2, 3, 4) is par...

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  13. Find the Cartesian equation of the line with passes through the point ...

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  14. Show that the lines (x-5)/7=(y+2)/(-5)=z/1andx/1=y/2=z/3 are perpendic...

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  15. Show that the line joining the origin to the point (2, 1, 1) is per...

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  16. Find the equation of a line parallel to x-axis and passing through the...

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  17. Find the angle between the following pairs of lines: -> r=(4 hat i- h...

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  18. Find the angle between the following pairs of lines: -> r=(3 hat i+2 ...

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  19. Find the angle between the following pairs of lines: -> r=lambda( hat...

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  20. Find the angle between the following pairs of line: (x+4)/3=(y-1)/5=(z...

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