Find the resultant of these two vectors: 2.00 x 102 units due east and 4.00 x 102 units 30.0° north of west.

If two vectors are represented both in magnitude and direction by the two adjacent sides of a triangle taken in an order, then their resultant is given by the third side taken in the reverse order.

Resultant vector :

                          R = sqrt of A^2 + B^2 + 2ABcosθ

given :

           A = 200 units

           B = 300 units

           θ = 30 degrees

∴ R = sqrt of 200^2 + 300^2 + 2(200)(300)cos35

the answer is 477.805656

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

the answer to this question is 3/19

step-by-step explanation: