Prove that if `vecu=u_1hati+u_2hatj` and `vecv=v_1hati+v_2hatj` are non-zero vectors, then they are parallel if and only if `u_1v_2-u_2v_1=0`.

Show that vectors vecA= hati - 5hatj and vecB= 2hati-10 hatj are parallel to each other.

Show that the vectors veca=2hati+3hatj and vecb=4hati+6hatj are parallel.

If veca=4hati-hatj+hatk and vecb= 2hati-2hatj+hatk , then find a unit vector parallel to the vector veca + vecb .

Let veca=hati+hatj+hatk , vecb=hati-hatj+hatk and vecc=hati-hatj-hatk be three vectors. A vector vecv in the plane of veca and vecb , whose projection on vecc is 1/sqrt3 , is given by :

veca=hati+hatj+hatk,vecb=2hati-hatj+3hatk,vecc=hati-2hatj+hatk then find a unit vectors parallel to vector 2veca-vecb+vecc .

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

If veca=5hati+hatj-4hatk, vecb=2hati-3hatj+hatk and vecc=hati+3hatj-2hatk then find a unit vector parallel to the vector 2veca+vecb+3vecc .

Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3hatk

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : veca_2-veca_1

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : vecb_2-vecb_1