Community Answer

NoTE:- If x=(x_(1),x_(2),cdots,x_(n))inR^(n) then the length or norm of the vector x is denoted by ||x|| and given by||x||=(:x,x:)^(1//2)=(sum_(i=1)^(n)x_(i)^(2))^(1//2)Solution:- (a): v=(:8,-theta:){:[:.quad||v||=(:v","v:)^(v_(2))=sqrt((theta)^(2)+(-theta)^(2))],[=thetasqrt2]:}{:[v=-3 hat(ı)+6 hat(ȷ)=(:-3","6:)],[:.quad||v||=sqrt((-3)^(2)+6^(2))],[=sqrt(9+36)],[=3sqrt5]:}(b)(C){:[v=(:-1","2","1:)],[:.quad||v||=sqrt((-1)^(2)+2^(2)+1^(2))],[=sqrt(1+4+1)=sqrt6]:}{:[" (d) "v^(2),=- hat(ı)+2 hat(ȷ)+3 hat(k)=(:-1","2","3:)],[:.quad||v||,=sqrt((-1)^(2)+2^(2)+3^(2))],[" Scanned with ",,=sqrt(1+4+9)=sqrt14]:}Solution:-Task:- Find thecomponent form ofthe vector v in2- space that has the length ||v||=6 and makes the angle theta=120^(@) with the positive x-axis.We know that{:[v=(:||v||cos theta","quad||v||sin theta:)],[=(:6cos 120^(@),6sin 120^(@):)],[=(:6*(-(1)/(2)),6(sqrt3//2):)],[=(:-3","3sqrt3:)]:}Solution:- Given that u=(:2,-3,1:),v=(:-5,4,2:)NoTE:- The scalar product (dot produet) of two non-zero vector vec(a) and vec(b), denoled by vec(a)* vec(b) is defined as vec(a)* vec(b)=| vec(a)|| vec(b)|cos theta,CSCamsewhere theta is the angle between vec(a) and vec(b),0 <= theta <= piScanned withIf either vec(a)=0 or v ... See the full answer