If `bar(a) and bar(b)` are two vectors perpendicular each other, prove that `(bar(a) + bar(b))^(2) = (bar(a) - bar(b))^(2)`

If bar(a) and bar(b) are two unit vectors perpendicular to each other and bar(c)=lambda_1 bar(a)+lambda_2bar(b)+lambda_(3)(bar(a)timesbar(b)) ,then which of the following is (are) true? (A) lambda_(1)=bar(a).bar(c) (B) lambda_(2)=|bar(b)timesbar(a)| (C) lambda_(3)=|(bar(a)timesbar(b))timesbar(c)| (D) lambda_(1)+lambda_(2)+lambda_(3)=(bar(a)+bar(b)+bar(a)timesbar(b)).bar(c)

If bar(a)=bar(i)+bar(j)+bar(k) , bar(b)=bar(i)+2bar(j)+3bar(k) then a unit vector perpendicular to both vectors (bar(a)+bar(b)) and (bar(a)-bar(b)) is

If bar(a),bar(b) are vectors perpendicular to each other and |bar(a)|=2,|bar(b)|=3, bar(c)timesbar(a)=b, then the least value of 2|bar(c)-bar(a)|" is

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) and bar(b) are unit vectors then the vectors (bar(a)+bar(b))xx(bar(a)xxbar(b)) is parallel to the vector

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

bar(a) & bar(b) are two non- collinear vectors then the value of {(bar(a))/(|bar(a)|^(2))-(bar(b))/(|bar(b)|^(2))}^(2) is equal to

If bar(a),bar(b) are two vectors of magnitude 2 and inclined at 60^(@), then (bar(a),bar(a)+bar(b))=