For any vector `bar(r)`, `(bar(r)*bar(i))bar(i)+(bar(r)*bar(j))bar(j)+(bar(r)*bar(k))bar(k)=`

If there vectors bar(a)=bar(i)+bar(j)+bar(k),bar(b)=bar(i)-2a^(2)bar(j)+bar(a) ,bar(c)=bar(i)+(a+1)bar(j)-abar(k) are linearly dependent vectors then the real 'a' lies in the interval.

If three vectors bar(a)=bar(i)+bar(j)+bar(k),bar(b)=bar(i)-2a^(2)bar(j)+abar(k),bar(c)=bar(i)+(a+1)bar(j)-abar(k) are linearly dependent vectors then the real a lies in the interval.

If there vectors bar(a)=bar(i)+bar(j)+bar(k) , bar(b)=bar(i)-2a^(2)bar(j)+abar(k) , bar(c)=bar(i)+(a+1)bar(j)-abar(k) are linearly dependent vectors then the real a lies in the interval.

If bar(a)bar(b)bar(c) are three non-zero and non-null sand is any vector in space,then [bar(b)bar(c)bar(r)]bar(a)+[bar(c)bar(a)bar(r)]bar(b)+[bar(a)bar(b)bar(r)]bar(c) is equal to

The lines bar(r)=bar(i)+bar(j)-bar(k)+s(3bar(i)-bar(j)) and bar(r)=4bar(i)-bar(k)+t(2bar(i)+3bar(k))

The vectors bar(i)+4bar(j)+6bar(k),2bar(i)+4bar(j)+3bar(k) and bar(i)+2bar(j)+3bar(k) form

bar(i)xx(bar(a)xxvec i)+bar(j)xx(bar(a)xxbar(j))+(bar(a)xx(bar(a)xxbar(j))+bar(k)(bar(a)xxbar(k))=

If bar(p)bar(q)bar(r) is reciprocal system of vector triad bar(a),bar(b) and bar(c) then [bar(a)bar(b)bar(c)][bar(p)bar(q)bar(r)]=

The shortest distance the two lines bar(r)=2bar(i)-bar(j)-bar(k)+lambda(2bar(i)+bar(j)+2bar(k)) and bar(r)=(bar(i)+2bar(j)+bar(k))+mu(bar(i)-bar(j)+bar(k)) is

The reciprocal of bar(a) where bar(a)=-bar(i)+bar(j)+bar(k),bar(b)=bar(i)-bar(j)+bar(k),bar(c)=bar(i)+bar(j)+bar(k) is