If the vectors AB=`hat i+3hat j+4hat k,AC=5hat i+hat j+2hat k` are two sides of a triangle ABC, whose centroid is G ,then |AG|=

If the vectors vec(A) B = 3 hat(i)+4 hat (k) and vec(AC) = 5 hat(i)-2 hat(j)+4hat(k) are the sides of a triangle ABC, then the length of the median through A is

If the vectors (hat(i) + hat(j) + hat(k)) and 3hat(i) form two sides of a triangle, then area of the triangle is :

Show that the vector 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k ,\ 3 hat i-4 hat j-4 hat k form the sides of a rights angled triangle.

If vector vec(A)=hat(i)+2hat(j)+4hat(k) and vec(B)=5hat(i) represent the two sides of a triangle, then the third side of the triangle can have length equal to

If vector vec(A)=hat(i)+2hat(j)+4hat(k) and vec(B)=5hat(i) represent the two sides of a triangle, then the third side of the triangle can have length equal to

Show that the vectors 2 hat i- hat j+ hat k , hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k form the vertices of a right angled triangle.

Find a vector of magnitude 49, which is perpendicular to both the vectors 2 hat i+3 hat j+6 hat k and 3 hat i-6 hat j+2 hat k . Find a vector whose length is 3 and which is perpendicular to the vector vec a=3 hat i+ hat j-4 hat k and vec b=6 hat i+5 hat j-2 hat k .

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

Show that the vectors vec a=3 hat i-2 hat j+ hat k , vec b= hat i+3 hat j+5 hat k , vec c=2 hat i+ hat j-4 hat k form a right angled triangle.