Show that the line through the points (4...

Show that the line through the points (4,7,8) and (2,3,4) is parallel to the vector `3hati+2hatj-2hatk`.

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Find the vector and the Cartesian equations of the line through the point (5, 2, – 4) and which is parallel to the vector 3hati+2hatj-8hatk

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3hati + 2hatj - 2hatk

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

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

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

The vector equation of the line passing through the points (3,5, 4) and (5, 8, 11) is vecr=3hati+5hatj+4hatk+lamda(2hati+3hatj+7hatk)

Find the equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the vectoer and cartesian equations of the line through the point (1,2,-4) and perpendicualr of the lines: vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) and vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-5hatk)

Let vecF=2hati+4hatj+3hatk at the point P with position vector hati-hatj+3hatk . Find the moment of vecF about the line through the origin O in the direction of the vector veca=hati+2hatj+2hatk .

Find the vector equation of the line through (4,3,-1) and parallel to the line: vecr=(2hati-hatj+3hatk)+lambda(3hati-hatj+4hatk)

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE

show that the three lines with direction cosines <12/13,-3/13,-4/13>, ...
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Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perp...
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Show that the line through the points (4,7,8) and (2,3,4) is parallel ...
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Find the equation of the line which passes through the point (1, 2, 3)...
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Find the equation of the line in vector and in cartesian form that pas...
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Find the cartesian equation of the line which passes through the point...
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The cartesian equation of a line is (x-5)/3 = (y+4)/7 = (z-6)/2. Write...
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Find the vector and the cartesian equations of the lines that passes t...
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Find the vector and the cartesian equations of the line that passes th...
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Find the angle between the following pair of lines: vecr = 2hati-5hatj...
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Find the angle between the following pair of lines: vecr = 3hati+hatj-...
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Find the angle between the following pair of lines: (x-2)/2=(y-1)/5=(z...
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Find the angle between the following pair of lines: x/2=y/2=z/1 and (x...
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Find the value of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2 and...
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Show that the lines (x-5)/7 = (y+2)/-5 = z/1 and x/1 = y/2 = z/3 are p...
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Find the shortest distance between the lines vecr = (hati + 2hatj+hatk...
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Find the shortest distance between the lines ((x+1)/7=(y+1)/-6=(z+1)/1...
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Find the shortest distance between the lines whose vector equations ar...
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Find the shortest distance between the following lines whose vector eq...
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In the following, determine the direction cosines of the normal to the...
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