The value of 'a' , for which the points A,B,C with position vectors `2vec(i)-vec(j)+vec(k), vec(i)-3vec(j)-5vec(k),` and ` avec(i)-3vec(j)+vec(k)` are vertices of a right angled triangle with `angleC=pi/2` are

The values of a for which the points A,B,C with position vectors 2vec i-vec j+vec k+vec i-3vec j-5vec k and avec i-3vec j+vec k,vec i-3vec j-5vec k and avec i-3vec j+vec k are the vertices of a right angled triangle with /_C=(pi)/(2) are

The area of the triangle formed by thepoints whose position vectors are 3vec(i) + vec(j), 5vec(i) + 2vec(j) + vec(k) and vec(i) -2vec(j) + 3vec(k) is (in sq.u)

The vector area of the triangle formed by the points vec(i) -vec(j) + vec(k), 2vec(i) + vec(j) -2vec(k) and 3vec(i) + vec(j) + 2vec(k) is

Examine if vec(i) - 3vec(j) + 2vec(k), 2vec(i) - 4vec(j) - vec(k) and 3vec(i) + 2vec(j) - vec(k) are linearly independent or dependent .

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

Find the angle between the vectors vec(i) + 2vec(j) + 3vec(k) and 3vec(i) - vec(j) + 2vec(k) .

Find the angle between the vectors : vec(a)=3vec(i)-2vec(j)+vec(k) and vec(b)=vec(i)-2vec(j)-3vec(k)

If vec(a)= 2vec(i) -vec(j) + 3vec(k), vec(b)= p vec(i) + vec(j) + q vec(k) and vec(b) xx vec(a) = vec(0) , then

If the projection of vec(i)+3vec(j)+7vec(k) on 2vec(i)-3vec(j)+6vec(k) is ___________.

Find the vector equation of the plane passing through the points. vec(i)-2vec(j)+5vec(k), -5vec(j)-vec(k) and -3vec(j)+5 vec(j) .