A vector oflength `sqrt7` which is perpendicul to `2bar j -bar k and -bar i+2bar j-3bar k` and makes obtus angle with y-aixs is

Find unit vector perpendicular to both bar(i) + bar(j) + bar(k) and 2bar(i) + bar(j) + 3bar(k) .

Find a vector of magnitude 6, which is perpendicualr to both the vectors 2bar(i)-bar(j)+2bar(k) and 4bar(i)-bar(j)+3bar(k) .

The vector bar(c) is perpendicular to both bar(a)=(bar(i)-2bar(j)+bar(k)),bar(b)=(2bar(i)+bar(j)-bar(k)),bar(c) also satisfies , |bar(c)times(bar(i)-bar(j)+bar(k))|=2sqrt(6) then bar(c)=

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

Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2bar(j) -3bar(k) , bar(j) - tbar(k) are coplanar.

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 :

A unit vector is coplanner with bar(i)+bar(j)+2bar(k) and bar(i)+2bar(j)+bar(k) and it is perpendicular to the vector bar(i)+bar(j)+bar(k) . Then the vector …………..

Find the vector equation of the plane which passes through the points 2bar(i)+4bar(j)+2bar(k), 2bar(i)+3bar(j)+5bar(k) and parallel to the vector 3bar(i)-2bar(j)+bar(k) . Also find the point where this plane meets the line joining the points 2bar(i)+bar(j)+3bar(k) and 4bar(i)-2bar(j)+3bar(k) .