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Statement 1: Lines vec r= hat i+ hat j-...

Statement 1: Lines ` vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i++3 hat k)` intersect. Statement 2: ` vec bxx vec d=0` , then lines ` vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d` do not intersect.

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Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) are coplanar. Also, find the plane containing these two lines.

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CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
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  2. The equation of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3)a n...

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  3. Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a...

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  4. Statement 1: Line (x-1)/1=(y-0)/2=(z2)/(-1) lies in the plane 2x-3y-4z...

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  5. What is the equation of the plane which passes through the z-axis and ...

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  7. Statement 1: Let theta be the angle between the line (x-2)/2=(y-1)/(-3...

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  8. If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,...

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  13. The x-y plane is rotated about its line of intersection with the y-...

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  14. Consider the planes 3x-6y+2z+5=0a n d4x-12+3z=3. The plane 67 x-162 y+...

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  15. A variable plane x/a+y/b+z/c=1 at a unit distance from origin cuts the...

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  17. The equation of the line x+y+z-1=0, 4x+y-2z+2=0 written in the symmetr...

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