if `bar(a),bar(b),bar(c)` are any three vectors then prove that `[bar(a),bar(b)+bar(c),bar(a)+bar(b)+bar(c)]=0`

If bar(a),bar(b)andbar(c) are any three vectors, prove that (1) [bar(a)+bar(b) bar(b)+bar(c) bar(c)+bar(a)]=2[bar(a)bar(b)bar(c)] (2) [bar(a) bar(b)+bar(c) bar(a)+bar(b)+bar(c)]=0

If bar(a),bar(b),bar(c) are any three vectors, prove that (1) [bar(a)+bar(b)" "bar(a)+bar(c)" "bar(b)]=[bar(a)" "bar(c)" "bar(b)] (2) [bar(a)-bar(b)" "bar(b)-bar(c)" "bar(c)-bar(a)]=0 .

If bar(a)+bar(b)+bar(c), then

If bar(a),bar(b),bar(c) be three vectors such that |bar(a)+bar(b)+bar(c)|=1,lambda(bar(a)xxbar(b)) and |bar(a)|=(1)/(sqrt(2)),|bar(b)|=(1)/(sqrt(3)),|bar(c)|=-(1)/(sqrt(6)) then the angle between bar(a) and is

If (bar(a)xxbar(b))xxbar(c)=bar(a)xx(bar(b)xxbar(c)), where bar(a),bar(b) and bar(c) are any three vectors such that bar(a)*bar(b)!=0,bar(b)*bar(c)!=0, then bar(a) and bar(c) are

bar(a) , bar(b) and bar(c) are three vectors such that bar(a) + bar(b) + bar(c) = bar(0) and |bar(a)| =2, |bar(b)| =3, |bar(c)| =5 ,then bar(a) . bar(b) + bar(b) . bar(c) + bar(c) . bar(a) equals

If bar(a),bar(b),bar(c) are three non zero vectors,then bar(a).bar(b)=bar(a).bar(c)rArr

If bar(a),bar(b),bar(c) are coplanar then the value of |[bar(a),bar(b),bar(c)],[bar(a)*bar(a),bar(a)*bar(b),bar(a)*bar(c)],[bar(b).bar(a),bar(b)*bar(b),bar(b)*bar(c)]|=

If bar(a),bar(b) and bar(c) are mutually perpendicular vectors 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.