A unit vector perpendicular to the vector `-bar(i)+2bar(j)+2bar(k)` and making equal angles with x and y- axis can be

The unit vector perpendicular to both of the vectors 2bar(i)-bar(j)+bar(k) and 3bar(i)+4bar(j)-bar(k) is.

A plane is at distance of 8units from the origin and is perpendicular to the vector 2bar(i)+bar(j)+2bar(k) then the equation of the plane is

The direction ratios of a line which is perpendicular to the two vectors -2bar(i) +3 bar(j) -bar(k) and 4 bar(i) +bar(j) +3 bar(k) is

A vector oflength sqrt(7) which is perpendicul to 2bar(j)-bar(k) and -bar(i)+2bar(j)-3bar(k) and makes obtus angle with y-aixs is

Vector bar(V) is perpendicular to the plane of vectors bar(a)=2i-3j+k and bar(b)=i-2j+3k and satisfy the condition bar(V)*(i+2j-7k)=10. Find |bar(V)|^(2)

If bar(P)=i+j+2k and bar(Q)=3i-2j+k ,the unit vector perpendicular to both bar(P) and bar(Q) is

If bar(a)=bar(i)+bar(j)+bar(k) , bar(b)=bar(i)+2bar(j)+3bar(k) then a unit vector perpendicular to both vectors (bar(a)+bar(b)) and (bar(a)-bar(b)) is

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 :

Let bar(a) and bar(b) be unit vector.If the vectors bar(c)=bar(a)+2bar(b) and bar(d)=5bar(a)-4bar(b) are perpendicular to the each other then angle between bar(a) and bar(b) is