`1.bar(5)+2.bar(6)+3.bar(7)=`

The value of 0.bar(3) + 0.bar(6) + 0. bar( 7 ) + 0. bar( 8 ) in fraction will be

The point of intersection of the lines bar(r)timesbar(a)=bar(b)timesbar(a) and bar(r)timesbar(b)=bar(a)timesbar(b) is 1. bar(a)-bar(b) 2. bar(a)+bar(b) 3. 2bar(a)+3bar(b) 4. 3bar(a)-2bar(b)

If [(bar(a)+2bar(b)+3bar(c))times(bar(b)+2bar(c)+3bar(a))].(bar(c)+2bar(a)+3bar(b))=54 , where bar(a),bar(b)&bar(c) are 3 non coplanar vectors then |[bar(a).bar(a)quad bar(a).bar(b)quad bar(a).bar(c)],[bar(b).bar(a)quad bar(b).bar(b)quad bar(b).bar(c)],[bar(c).bar(a)quad bar(c).bar(b)quad bar(c).bar(c)]|

If |bar(a)|=1,|bar(b)|=2,(bar(1),bar(b))=(2 pi)/(3) , then |(bar(a)+3bar(b))times(3bar(a)-bar(b))|^(7)=

Show that points with p.v bar(a)-2bar(b)+3bar(c ),-2bar(a)+3bar(b)-bar(c ),4bar(a)-7bar(b)+7bar(c ) are collinear. It is given that vectors bara,barb,bar c are non-coplanar.

Let bar(a),bar(b),bar(c) are three non-coplanar vectors such that bar(r)_(1)=bar(a)-bar(b)+bar(c);bar(r)_(2)=bar(b)+bar(c)-bar(a);bar(r)_(3)=bar(c)+bar(a)+bar(b),bar(r)=2bar(a)-3bar(b)+4bar(c) .If bar(r)=lambda_(1)bar(r)_(1)+lambda_(2)bar(r)_(2)+lambda_(3)bar(r)_(3) then lambda_(1)+lambda_(2)+lambda_(3) is equal to

If |bar(a)|=|bar(b)|=|bar(c)|=2 , and bar(a)*bar(b)=bar(b).bar(c)=bar(c)*bar(a)=2 then [bar(a) bar(b) bar(c)] = (1). 3sqrt(2) (2). 4sqrt(2) (3).32 (4).48

If bar(a) is a perpendicular to bar(b) and bar(c), |bar(a)|=2, |bar(b)|=3, |bar(c)|=4 and the angle between bar(b) and bar(c) is (2pi)/(3) then |[bar(a) bar(b) bar(c)]| =

If bar(a),bar(b),bar(c) are non - coplanar vectors, then show the vectors -bar(a)+3bar(b)-5bar(c),-bar(a)+bar(b)+bar(c) and 2bar(a)-3bar(b)+bar(c) are coplanar.

bar (a) = 2bar (i) + 3bar (j) -bar (k), bar (b) = bar (i) + 2bar (j) -4bar (k), bar (c) = bar (i) + bar (j) + bar (k), bar (d) = bar (i) -bar (j) -bar (k) then