Find the vector w which answer the conditions u*y = 14 and v*w = 16 where u and v vectors ; u = 3i + j and v = 5i -2j

Expert Answers
hala718 eNotes educator| Certified Educator

u= 3i+j

v=5i-2j

we know that v*y=14

==> v*y= 3x+y=14...(1)

we also have u*w =16

==> u*w= 5x-2y=16....(2)

From (1) and (2) we obtains:

y= 14-3x

5x-2y=16 ==> 5x-2(14-3x)=16

==> 5x-28 +6x=16

==> 11x= 44==> x=4

y=14-3(4)= 14-12= 2

then w = 4i +2j

==> y=

neela | Student

To find , w such that u*w=14, v*w = 16, where u =3i+j and v = 5i-2j.

Solution:

Let w = ai+bj.

Then u*w = (3i+j)*(ai+bj) =

=3a+b = 14.........(1)

v*w = (5j-2j)*(ai+bj) =

5a-2b = 16...........(2)

solving for and b from eq(1) and eq(2):

2*Eq(1)+eq(2) gives: 6a+5a = 28+16= 44. Or

11a = 44. Or a = 44/11 = 4.

Substituting a = 4 in eq(2), we get:

5*4 -2b = 16.Or

-2b = 16-20 = -4. Or

b = -4/(_2) = 2.

So w = 4i+2j

giorgiana1976 | Student

6.       Using the definition of dot product and the facts from hypothesis we'll obtain the following system:

3x + y = 14 => y = 14 - 3x

5x - 2y = 16 => 5x - 2 (14 - 3x) = 16 => 5x - 28 + 6x - 16 = 0

11x = 44 => x = 4

y = 14 - 3*4

y = 14 - 12

y=2

So, the vector  w = 4*i + 2*j