माना bar(u)=bar(i)+bar(j),bar(v)=bar(i)-bar(j) व bar(w)=bar(i)+2bar(j) हैं | यदि एकांक सदिश bar(...

Let bar(u)=bar(i)+bar(j),bar(v)=bar(i)-bar(j),bar(w)=bar(i)+2bar(j)+3bar(k) .If bar(n) is a unit vector such that bar(u).bar(n)=0,bar(v).bar(n)=0 then |bar(w).bar(n)|=

Given three vectors bar(a)=6bar(i)-3bar(j),bar(b)=2bar(i)-6bar(j) and bar(c)=-2bar(i)+21bar(j) such that bar(alpha)=bar(a)+bar(b)+bar(c) Then the resolution of the vector bar(alpha) into components with respect to bar(a) and bar(b) given by

If bar(a)=bar(i)+2bar(j)+bar(k) , (b)=bar(i)-bar(j)+bar(k) and bar(c)=bar(i)+bar(j)-bar(k) . A vector in the plane of bar(a) and bar(b) whose projection on bar(c) is (1)/(sqrt(3)) is

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))

If bar(a)=2bar(i)+3bar(j),bar(b)=bar(i)+bar(j)+bar(k),bar(c)=3bar(i)+lambdabar(j)+2bar(k) and [bar(a)bar(b)bar(c)]=-1 then lambda

If bar(a)=2bar(i)+3bar(j),bar(b)=bar(i)+bar(j)+bar(k),bar(c)=3bar(i)+lambdabar(j)+2bar(k) and [bar(a)bar(b)bar(c)]=-1 then lambda

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.

Let bar(a)=-bar(i)-bar(k),bar(b)=-bar(i)+bar(j) and bar(c)=bar(i)+2bar(j)+3bar(k) be three given vectors. If bar(r) is a vector such that bar(r) times bar(b)=bar(c) times bar(b) and bar(r).bar(a)=0 then bar(r).bar(b)=

Consider the parallelopiped with sides bar(a)=3bar(i)+2bar(j)+bar(k),bar(b)=bar(i)+bar(j)+2bar(k) and bar(c)=bar(i)+3bar(j)+3bar(k) then angle between bar(a) and the plane containing the face determined by bar(b) and bar(c) 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