`bar(a),bar(b)` and `bar(c)` are unit vectors satisfying `|bar(a)-bar(b)|^(2)+|bar(b)-bar(c)|^(2)+|bar(c)-bar(a)|^(2)=9` then `|2bar(a)+5bar(b)+5bar(c)|=`

Suppose bar(a), bar(b), bar(c) be three unit vectors such that |bar(a)-bar(b)|^(2)+|bar(b)-bar(c)|^(2)+|bar(c)-bar(a)|^(2) is equal to 3 . If bar(a), bar(b), bar(c) are equally inclined to each other at an angle:

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) and bar(c) are perpendicular,bar(c)+bar(a),bar(b)+bar(c) and bar(a)+bar(b)+ respectively and if |bar(a)+bar(b)|=6,|bar(b)+bar(c)|=8 and |bar(c)+bar(a)|=10 then |bar(a)+bar(b)+bar(c)| is equal to

Let bar(a),bar(b),bar(c) be three vectors satistying bar(a)xxbar(b)=2bar(a)xxbar(c),|bar(a)|=|bar(c)|=1bar(b)=4 and |bar(b)xxbar(c)|=sqrt(15). If bar(b)-2bar(c)=lambdabar(a) then lambda is

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

(bar(a)+2bar(b)-bar(c))*(bar(a)-bar(b))xx(bar(a)-bar(bar(c)))=

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),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)|=2 and bar(a).bar(b)=bar(b).bar(c)=bar(c).bar(a)=2 then [bar(a) bar(b) bar(c)] equal to