If `hata=5hati-hatj-3hatK` and `vecb=hati+3hatj-5hatk`, then show that the vectors `veca+vecb` and `veca-vecb` are perpendicular.

If vecA=3hati+2hatj and vecB=4hatj-5hatk then find |vecA+vecB|

If vecA=3hati+2hatj and vecB=4hatj-5hatk then find |vecA-vecB|

The values of x for which the angle between the vectors veca =xhati - 3hatj-hatk and vecb = 2x hati + x hatj -hatk is acute, and the angle, between the vector vecb and the axis of ordinates is obtuse, are

Let veca=hati+2hatjandvecb=2hati+hatj . Is |veca|=|vecb| ? Are the vectors vecaandvecb equal?

Let veca = hatj - hatk and vecc = hati - hatj - hatk. Then the vector vecb satisfying veca xx vecb + vecc= vec0 and veca. Vecb=3 is :

The projection of veca=3hati-hatj+5hatk on vecb=2hati+3hatj+hatk is

Statement 1 : Let A(veca), B(vecb) and C(vecc) be three points such that veca = 2hati +hatk , veb = 3hati -hatj +3hatk and vecc =-hati +7hatj -5hatk . Then OABC is tetrahedron. Statement 2 : Let A(veca) , B(vecb) and C(vecc) be three points such that vectors veca, vecb and vecc are non-coplanar. Then OABC is a tetrahedron, where O is the origin.

If veca = ( 2 hati + 3 hatj + hatk ) then write the direction cosines of veca

If veca = 4 hati + 6 hatj and vecb =3 hatj + 4 hatk, then the vector form of the component of veca along vecb is :