If `veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk` and `vecc=hati+alphahatj+betahatk`
are linearly dependent vectors and `|vecc|=sqrt(3)` then:

If vector vec a = hati + hatj + hatk , vecb = 4 hati + 3 hatj + 4 hatk and vec c = hati + alpha hatj + beta hatk are linearly dependent and | vec c | = sqrt3 , then value of | alpha | + | beta | is

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

If veca=hati-2hatj+3hatk, vecb=2hati+3hatj-hatk and vecc=rhati+hatj+(2r-1)hatk are three vectors such that vecc is parallel to the plane of veca and vecb then r is equal to,

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 .

If veca=7hati+3hatj-6hatk , vecb=2hati+5hatj-hatk and vecc=-hati+2hatj+4hatk . Find (veca-vecb)xx(vecc-vecb) .

If vecA= hati+2hatj+3hatk, vecB=-hati+hatj + 4hatk and vecC= 3hati-3hatj-12hatk , then find the angle between the vector (vecA+vecB+vecC) and (vecAxx vecB) in degrees.

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

If veca =hati + hatj-hatk, vecb = - hati + 2hatj + 2hatk and vecc = - hati +2hatj -hatk , then a unit vector normal to the vectors veca + vecb and vecb -vecc , is

If vectors veca =hati +2hatj -hatk, vecb = 2hati -hatj +hatk and vecc = lamdahati +hatj +2hatk are coplanar, then find the value of lamda .