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

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

The vector equation of the line passing through the point vec(i)-2vec(j) + vec(k) and perpendicular to the vectors 2vec(i)-3vec(j)-vec(k), vec(i) + 4vec(j)-2vec(k) is

A unit vector normal to the plane through the points vec(i), 2vec(j) and 3vec(k) is

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

Find the unit vectors perpendicular to both the vectors 2vec(i)- 3vec(j) + 5vec(k) and -vec(i) + 4vec(j) + 2vec(k)

The Cartesian equation of the plane passing through the point (3,-2,-1) and parallel to the vectors vec b=i-2j+4k and vec c=3i+2j-5k

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=__________.

Find a vector of magnitude and perpendicular to both the vectors vec(a)= 2vec(i)- 2vec(j) + vec(k) and vec(b)= 2vec(i) + 2vec(j) + 3vec(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)

Find the unit vector in the direction of the vector vec a + vec b if vec a =vec i +2 vec j + 3 vec k and vec b = 2 vec i + 3 vec j + 5 vec k .