Let `bar(a)=bar(i)+bar(j)+bar(k),bar(b)=bar(i)-bar(j)+2bar(k)` and `bar(c)=xbar(i)+(x-2)bar(j)-bar(k)` .If the vector `bar(c)` lies in the plane of `bar(a)` and `bar(b)` ,then x equals to

(bar(a)*bar(i))^(2)+(bar(a)*bar(j))^(2)+(bar(a)*bar(k))^(2)=

Let bar a= hat i+ hat j+ hat k ,""b= hat i- hat j+2 hat k and bar c=x hat i+(x-2) hat j- hat k . If the vector c lies in the plane of a and b , then x equals (1) 0 (2) 1 (3) -4 (4) -2

Evaluate : 2.bar(7)+1.bar(3)

In the Boolean algebra bar(A).bar(B) equals

In the circle above with diameter d, chords bar(PQ) and bar(TU) are parallel to diameter bar(RS) . If bar(PQ) and bar(TU) are each (3)/(4) of the length of bar(RS) , what is the distance between chords bar(PQ) and bar(TU) in terms of d?

If vec(A)=-hat(i)+ x hat(j) - 3 hat(k) and vec(B) = 2hat(i) - hat(k) then the value(s) of x for which the dot product of bar(A) & bar(B) is equal to unity :

Evaluate : 1.bar(45)+0.bar(3)

If (|veca+vecb|)/(|veca-vecb|)=1 , then angle between bar(a)" and "bar(b) is :-

Show that points with p.v bar(a)-2bar(b)+3bar(c ),-2bar(a)+3bar(b)-bar(c ),4bar(a)-7bar(b)+7bar(c ) are collinear. It is given that vectors bara,barb,bar c are non-coplanar.

The resultant of the three vectors bar(OA),bar(OB) and bar(OC) shown in figure :-