The vectors `2hati-mhatj+3hatk` and `(1+m)hati-2mhatj+hatk` include an acute angle for

Show that the vectors 2hati-hatj+hatk and hati-3hatj-5hatk are at righat angles.

If theta is the angle between two vectors hati-2hatj+3hatk and 3hati-2hatj+hatk , find sin theta

The vector (s) equally inclined to the vectors hati-hatj+hatk and hati+hatj-hatk in the plane containing them is (are_ (A) (hati+hatj+hatk)/sqrt(3) (B) hati (C) hati+hatk (D) hati-hatk

If the magnitude of the projection of the vector hati-hatj+2hatk on the vector perpendicular to the plane containing the vectors 2hati+hatj+3hatk and hati-hatj-2hatk is k, then the value of (1)/(k^(2)) is equal to

Using dot product of vectors show that the vectors 2hati-hatj+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk form a righat angled triangle

If theta is the angle between the vectors 2hati-2hatj+4hatk and 3hati+hatj+2hatk , then sin theta is equal to

The scalar product of the vector hati+hatj+hatk with a unit vector along the sum of the vectors 2hati+4hatj-5hatk and lamda hati+2hatj+3hatk is equal to one. Find the value of lamda .

If veca=hati+hatj+hatk, vecb=2hati-hatj+3hatk and vecc=hati-2hatj+hatk find a unit vector parallel to ther vector 2veca-vecb+3c .

The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk

The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk