If the vector `-bar(i)+bar(j)-bar(k)` bisects the angles between the vector `bar(c)` and the vector `3bar(i)+4bar(j)` ,then the unit vector in the direction of `bar(c)` is

If the vector bar(i)-bar(j)+bar(k) bisects the angle between the vector bar(a) and the vector 4bar(i)+3bar(j) , then the unit vector in the direction of bar(a) is (xbar(i)+ybar(j)+zbar(k)) then x-15y+5z is equal to

A vector of magnitude 3 , bisecting the angle between the vectors bar(a)=2i+j-k and, bar(b)=i-2j+k is-

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

The angle between the vectors bar(A) and bar B , where bar(A)=hat i+2hat j-hat k and bar(B)=-hat i+hat j-2hatk is

If lambda(2bar(i)-4bar(j)+4bar(k)) is a unit vector then lambda=

Let vec a be vector parallel to line of intersection of planes P_(1) and P_(2) through origin.If P_(1) is parallel to the vectors 2bar(j)+3bar(k) and 4bar(j)-3bar(k) and P_(2) is parallel to bar(j)-bar(k) and 3bar(I)+3bar(j), then the angle between vec a and 2bar(i)+bar(j)-2bar(k) is :

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 bar(a)=4bar(i)+6bar(j) and bar(b)=3bar(j)+4bar(k), then the vector form of the component of a along b is

The vector bar(i)+xbar(j)+3bar(k) is rotated through an angle theta and doubled in magnitude,then it becomes 4bar(i)+(4x-2)bar(j)+2bar(k) the value of x is

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