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A B C D is a parallelogram the position ...

`A B C D` is a parallelogram the position vectors of the points `A ,\ B ,\ a n d\ C` are respectively, `4 hat i+5 hat j-10 hat k ,\ 2 hat i-3 hat j+4 hat k\ a n d- hat i+2 hat j+ hat kdot` Find the vector equation of the line `B Ddot` Also, reduce it to Cartesian form.

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Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\ 2 hat i+3 hat j- hat k\ a n d- hat i-2 hat j+2 hat k

The position vectors of the points P ,\ Q ,\ R are hat i+2 hat j+3 hat k ,\ -2 hat i+3 hat j+5 hat k\ a n d\ 7 hat i- hat k respectively. Prove that P ,\ Q\ a n d\ R are collinear points.

Find the sum of vectors vec a= hat i-2 hat j+ hat k ,\ vec b=-2 hat i+4 hat j+5 hat k\ a n d\ vec c= hat i-6 hat j-7 hat kdot

If vec a= hat i+ hat j+ hat k ,\ vec b=2 hat i- hat j+3 hat k\ a n d\ vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec c

If vec a= hat i+ hat j- hat k ,\ vec b=- hat i+2 hat j+2 hat k\ a n d\ vec c=- hat i+2 hat j- hat k , then a unit vector normal to the vectors a+b\ a n d\ b-c is

The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and 4 hat i+5 hat j+lambda hat k , respectively. If the points A ,B ,C and D lie on a plane, find the value of lambda .

Write the projection of vec b+ vec c\ on\ vec a , when vec a=2 hat i-2 hat j+ hat k ,\ vec b= hat i+2 hat j-2 hat k\ a n d\ vec c=2 hat i- hat j+4 hat kdot

Find the vector equation of the plane passing through the points having position vectors hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

Find a unit vector perpendicular to both the vectors 4 hat i- hat j+3 hat k\ a n d-2 hat i+ hat j-2 hat kdot

RD SHARMA ENGLISH-STRAIGHT LINE IN SPACE -All Questions
  1. Find the vector equation of a line which is parallel to the vector 2 h...

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  2. A line passes through the point with position vector 2 hat i-3 hat j+4...

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  3. A B C D is a parallelogram the position vectors of the points A ,\ B ,...

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  4. Find the vector form as well as in Cartesian form, the equation of the...

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  5. Find the vector equation for the line which passes through the point ...

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  6. The Cartesian equations of a line are (x-5)/3=(y+4)/7=(z-6)/2dot Find ...

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

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  8. Find the direction cosines of the line (4-x)/2=y/6=(1-z)/3dot Also, re...

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

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

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

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

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

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

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

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

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

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

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

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