The `vec x` which is perpendicular to (2,-3,1) and (1,-2,3) and which satisfies the condition `vec x .(vec i + 2 vec j - 7 vec k) = 10`

Find a unit vector which is perpendicular to each of the vectors 3vec i+2vec j-vec k and 12vec i+5vec j-5vec k

Vector of length of 3 unit which is perpendicular to vec i + vec j + vec k and lies in the plane of vec i + vec j + vec k and 2vec i-3vec j, is (1) (3) / (sqrt ( 6)) (vec i-2vec j + vec k) (2) (3) / (sqrt (6)) (2vec i-vec j-vec k) (3) (3) / (sqrt (114)) ( 8vec i-7vec j-vec k) (4) (3) / (sqrt (114)) (- 7vec i + 8vec j-vec k)

Any vector which is perpendicular to each of the vectors 2vec(i) + vec(j) -vec(k) and 3vec(i) -vec(j) + vec(k) is normal to

A vector of magnitude 6 which is perpendicular to both 4vec(i) - vec(j) + 3vec(k) and -2vec(i) + vec(j) - 2vec(k) is

A vector vec( c) perpendicular to the vectors 2vec(i) + 3vec(j)-vec(k) and vec(i)-2vec(j)+3vec(k) satisfying vec(c ).(2vec(i)-vec(j) +vec(k))=-6 is

If the vector vec a= x vec i + y vec j + 2 vec k is perpendicular to the vector vec b = vec i - vec j + vec k and the scalar product of vec a and vec c= vec i + 2 vec j is equal to 4 then x= ________ and y=__________.

The cartesian equation of the plane perpendicular to vector 3vec i-2vec j-2vec k and passing through the point 2vec i+3vec j-vec k i

A point on the line r=2vec i+3vec j+4vec k+t(vec i+vec j+vec k) is

The sine of the angle between the vectors vec i+3vec j+2vec k and 2vec i-4vec j+vec k is

If vec(a).vec(i)=4 , then (vec(a) . vec(j))xx (2vec(j)-3vec(k)) =