4 ll3u 2vl j and w 12i 5j find 6 Unit vector for v 7 llvll l

4. ll3u 2vl j and w 12i 5j, find 6. Unit vector for v 7. llvll llwll si tolv 69 he two vectors v and w and determine if they are parallel, orthogonal,

Solution

9. v=2i+3j   w= 3i + 4j

   v.w= IvI IwI cos theta

v.w= 2*3 + 3*4 = 18

IvI = sqrt(2²+3²) = sqrt13

Iw)=sqrt(3²+4²) = 5

18 = sqrt 13    * 5 cos theta

18/5sqrt13=cos theta

theta=cos^-1(18/5sqrt13)

Here theta is neither 0 nor pi/2

Hence the vectors are neither parallel nor orthogonal