Show that the line , vecr=hati+hatj+lamb...

Show that the line , `vecr=hati+hatj+lambda(2hati+hatj+4hatk)` lies in the plane `vecr*(hati+2hatj-hatk)=3`.

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Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

State when the line vecr=veca+lambdavecb is parallel to the plane vecr*vecn=d . Show that the line vecr=hati+hatj+lambda (2hati+hatk+4hatk) is parallel to the plane vecr*(-2hati+hatk)=5 . Also, find the distance between the line and the plane.

Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the angle between the line : vecr=(hati-hatj+hatk)+lambda(2hati-hatj+3hatk) and the plane vecr*(2hati+hatj-hatk)=4 . Also find whether the line is parallel to the plane or not.

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =4.

True or false The line vecr=2hati-3hatj+hatk+t(hati-hatj+2hatk) lies in the plane vecr.(3hati+hatj-hatk)-2=0 .

Find the distance of the point (2,12,5) from the point of intersection of the line: vecr=2hati-4hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr*(hati-2hatj+hatk)=0 .

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

Find the angles between the line vecr=-hati+hatj+2hatk+lambda(3hati+2hatj+4hatk) and the plane vecr.(2hati+hatj-3hatk)+4=0

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE

The equation of the plane passing through the line of intersection of ...
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The point P is the intersection of the straight line joining the point...
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If the lines (x-2)/1=(y-3)/1=(z-4)/(-k) and (x-1)/k=(y-4)/2=(z-5)/1 ar...
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Distance between two parallel planes 2x+y+2z=8 and 4x+2y+4z+5=0 is
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The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z...
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The angle between the lines whose direction cosines satisfy the equa...
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The distance of the point (1,0,2) from the poitn of intersection of th...
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The equation of the plane containing the line 2x-5y+z=3, x+y+4z=5 and ...
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If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the place, l x+m y-z=9...
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The distance of the point (1, -5, 9) from the plane x-y+z=5 measured a...
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If a line has direction ratios <2,-1,-2>, then what are its direction ...
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Find the Cartesian equation of the following plane: vecr cdot (hati+ha...
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Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in t...
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Find the area of the triangle whose vertices are : A(1,2,3), B(2,-1,4)...
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Find the equations of the straight line passing through the point (2,...
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Find the image of the point (1,6,3) in the line : x/1=(y-1)/2=(z-2)/3.
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Find the equation of the plane passing through the point(-1, 3, 2) and...
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Prove that if a plane has intercepts a,b,c and is at a distance of p u...
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A line makes angles alpha, beta, gamma, delta with the diagonals of a ...
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Show that the lines (x-a+d)/(alpha-delta) = (y-a)/alpha = (z-a-d)/(alp...
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