If the vectors `bar(a)=2bar(i)+3bar(j)+6bar(k)` and `bar(b)` are collinear and `|bar(b)|=21`, then `bar(b)` equals to

If the vectors bar(a)=-2bar(i)+3bar(j)+ybar(k) and bar(b)=xbar(i)-6bar(j)+2bar(k) are collinear, then the value of x+y is

Let bar(a),bar(b) and bar(c) be three non-zero vectors,no two of which are collinear.If the vectors bar(a)+2bar(b) is collinear with bar(c) and bar(b)+3bar(c) is collinear with bar(a), then bar(a)+2bar(b)+6bar(c) is equal to

If the vectors bar(a)=-2bar(i)+3bar(j)+ybar(k) and bar(b)=xbar(i)-6bar(j)+2bar(k) are collinear,then the value of x+y is

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

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

The vector bar(b)=3bar(i)+4bar(k) is to be written as sum of a vector bar(b)_(1) parallel to bar(a)=bar(i)+bar(j) and a vector bar(b)_(2) perpendicular to bar(a) then bar(b)_(1) is equal to

Let bar(a) be a unit vector bar(b)=2bar(i)+bar(j)-bar(k) and bar(c)=bar(i)+3bar(k) then maximum value of [bar(a)bar(b)bar(c)] is

Let bar(a) be a unit vector bar(b)=2bar(i)+bar(j)-bar(k) and bar(c)=bar(i)+3bar(k) then maximum value of [[bar(a),bar(b),bar(c)]] is

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.

bar(a) and bar(b) are non-collinear vectors. If bar(c)=(x-2)bar(a)+bar(b) and bar(d)=(2x+1)bar(a)-bar(b) are collinear, then find the value of x.