If `bar(a), bar(b), bar(c)` are noncoplanar, find the point of intersection of the line passing through the points `2bar(a)+3bar(b)-bar(c), 3bar(a)+4bar(b)-2bar(c)` with the line joining the points `bar(a)-2bar(b)+3bar(c) and bar(a)-6bar(b)+6bar(c)`.

The vector equation of the line joining the points 3bar(i)+2bar(j)-4bar(k), 5bar(i)+4bar(j)-6bar(k) is

The points 2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5bar(c) are

The point of intersection of the lines bar(r)=bar(a)+t(bar(b)+bar(c)), bar(r)=bar(b)+s(bar(c)+bar(a)) is

Find the position vector of the midpoint of the line segment joining 3bar(a)+2bar(b)-c, bar(a)-4bar(b)+5bar(c) .

Find the equation of the line passing through the point 2bar(i)+3bar(j)-4bar(k) and parallel to the vector 6bar(i)+3bar(j)-2bar(k) in cartesian form.

If bar(a), bar(b), bar(c) are non coplanar vectors, then test for the collinearity of the following points whose position vectors are given. i) bar(a)-2bar(b)+3bar(c), 2bar(a)+3bar(b)-4bar(c), -7bar(b)+10bar(c) ii) 3bar(a)-4bar(b)+3bar(c), -4bar(a)+5bar(b)-6bar(c), 4bar(a)-7bar(b)+6bar(c) iii) 2bar(a)+5bar(b)-4bar(c), bar(a)+4bar(b)-3bar(c), 4bar(a)+7bar(b)-6bar(c)

If bar(a), bar(b), bar(c) are linearly independent vectors, then show that bar(a)-3bar(b)+2bar(c), 2bar(a)-4bar(b)-bar(c), 3bar(a)+2bar(b)-bar(c) are linearly independent.

i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that the vectors 5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c) are coplanar.