Assuming we are working in a real 3 dimensional inner product space (otherwise the inner product would not be defined by angles), we have that
v*w=||v||.||w||costhetav⋅w=||v||.||w||cosθ, where thetaθis the angle (in degrees) between v and w.
So v*w=3xx4xxcos68,755^@=4,348v⋅w=3×4×cos68,755∘=4,348
To find v+wv+w you will need to know what the co-ordinates of each vector is as you currently just have their norms.
Then you can add them according to the rules and obtain
v=(v_1,v_2,v_3) and w=(w_1,w_2,w_3) =>v=(v1,v2,v3)andw=(w1,w2,w3)⇒
v+w=(v_1+w_1,v_2+w_2,v_3+w_3)v+w=(v1+w1,v2+w2,v3+w3)
Then ||v+w||=sqrt((v_1+w_1)^2+(v_2+w_2)^2+(v_3+w_3)^2||v+w||=√(v1+w1)2+(v2+w2)2+(v3+w3)2
Similarly, ||4v-4w||=4sqrt((v_1-w_1)^2+(v_2-w_2)^2+(v_3-w_3)^2)||4v−4w||=4√(v1−w1)2+(v2−w2)2+(v3−w3)2
Alternatively, you may use the cosine rule since we are working in RR^3 and this will yield :
||v+w||^2=||v||^2+||w||^2-2||v||||w||cos68,755^@
therefore||v+w||=sqrt(3^2+4^2-2*3*4cos68,755^@)=4,038
||4v-4w||=4||v-w||=4||v+(-w)||=4||v+w||=4xx4,038=16,152
