If `veca=i-2j+3k, vecb=2i+3j-5k`, prove that `vecaandvecaxxvecb` are perpendicular.

If veca=5 hat i- hat j-3 hat k and vecb= hat i+3 hat j-5 hat k then show that the vectors veca+ vecb and veca- vecb are perpendicular.

If veca=2 hat i+2 hat j+3 hat k , vecb=- hat i+2 hat j+ hat k and vecc=3 hat i+ hat j are such that veca+lambda vecb is perpendicular to vecc , then find the value of lambda .

Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplanar. If vecc is pependicular to veca . Then vecc is

If veca=i+j+k,veca.vecb=1 and vecaxxvecb=j-k , then : vecb =

If vecP=i+j+2k and vecQ=3i-2j+k , the unit vector perpendicular to both vecP and vecQ is

if vecA=i-j, vecB=i+j+k are two vectors and vecC is another vector such that vecAxxvecC+vecB=vec0 and vecA.vecC=0 then |vecC|^(2)= (a) 9 (b) 8 (c) (3)/(2) (d) (17)/(2)

If veca= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k and vecc= hat i-2 hat j+ hat k find a unit vector parallel to the vector 2 veca- vecb+3 vecc .

If veca = hat i+ hat j+ hat k , vecb=2 hat i- hat j+3 hat k and vecc= hat i-2 hat j+ hat k find a unit vector parallel to the vector 2 veca- vec b+3 vecc .

Show that the vectors veca= hat i-2 hat j+3 hat k , vecb=-2 hat i+3 hat j-4 hat ka n d vec c= hat i-3 hat j+5 hat k are coplanar.

Show that the points A, B and C with position vectors, veca=3 hat i-4 hat j-4 hat k , vecb=2 hat i- hat j+ hat k and vecc= hat i-3 hat j-5 hat k respectively form the vertices of a right angled triangle.