Let `bar(a)`=(1,1,-1),`bar(b)`=(5,-3,-3) and `bar(c)`=(3,-1,2). If `bar(r)` is collinear with `bar(c)` and has length `(|bar(a)+bar(b)|)/(2)` then `bar(r)`

The vectors bar(a),bar(b)&bar(c) each two of which are non collinear. If bar(a)+bar(b) is collinear with bar(c),bar(b)+bar(c) is collinear with bar(a)&|bar(a)|=|bar(b)|=|bar(c)|=sqrt(2) .Then the value of |bar(a).bar(b)+bar(b).bar(c)+bar(c).bar(a)|=

If bar(c) = 3 bar(a) - 2 bar(b) then prove that [(bar(a),bar(b),bar(c))] = 0

If bar(a)=(2,1,-1),bar(b)=(1,-1,0),bar(c)=(5,-1,1) then the unit vector parallel to bar(a)+bar(b)-bar(c) , but in the opposite direction is

If (bar(a),bar(b))=(pi)/(6),bar(c) is perpendicular to bar(a) and bar(b),|bar(a)|=3,|bar(b)|=4,|bar(c)|=6 then |[bar(a)bar(b)bar(c)]|

Let bar(a),bar(b) and bar(c) be three non-zero vectors,no two of which are collinear.If the vectors bar(a)+2bar(b) is collinear with bar(c) and bar(b)+3bar(c) is collinear with bar(a), then bar(a)+2bar(b)+6bar(c) is equal to

If bar(a)=(2,1,-1),bar(b)=(1,-1,0),bar(c)=(5,-1,1) then the unit vector parallel to bar(a)+bar(b)-bar(c) , but in opposite direction is

If bar(a)=(2,1,-1),bar(b)=(1,-1,0),bar(c)=(5,-1,1) then the unit vector parallel to bar(a)+bar(b)-bar(c) , but in opposite direction is

If bar(a)=(2,1,-1),bar(b)=(1,-1,0),bar(c)=(5,-1,1) then the unit vector parallel to bar(a)+bar(b)-bar(c) but in the opposite direction is

If bar(a)=(2,1,-1),bar(b)=(1,-1,0),bar(c)=(5,-1,1) then the unit vector parallel to bar(a)+bar(b)-bar(c) but in the opposite direction is

If bar(a)=(2,1,-1),bar(b)=(1,-1,0),bar(c)=(5,-1,1) then the unit vector parallel to bar(a)+bar(b)-bar(c) but in the opposite direction is