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)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 then prove that [bar(a),bar(b)+bar(c),bar(a)+bar(b)+bar(c)]=0

If [bar(a)+2bar(b)2bar(b)+bar(c)5bar(c)+bar(a)]=k[bar(a)bar(b)bar(c)]

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) and bar(c) are mutually perpendicular vectors then [bar(a)bar(b)bar(c)]=

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 non-coplanar vectors such that then bar(b)xxbar(c)=bar(a),bar(c)xxbar(a)=bar(b) and bar(a)xxbar(b)=bar(c), then |bar(a)+bar(b)+bar(c)|=

bar a, bar b, bar c are three vectros, then prove that: (bar a xx bar b) xx bar c = (bar a. bar c) bar b-(bar b. bar c) bar a.

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)+2bar(b)+3bar(c)=bar(0) then bar(a)xxbar(b)+bar(b)xxbar(c)+bar(c)xxbar(a)=