vectorsFind the vector v if u*v=15, w*v=17, u=5i+2j, w=i-j .

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The vector v has to be determined given that u*v=15, w*v=17, u=5i+2j, w=i-j

Let v = ai + bj

u*v = 5a + 2b = 15

w*v = a - b = 17

5a + 2b + 2a - 2b = 15 + 34

=> 7a = 49

=> a = 7

b = -10

The vector v = 7i - 10j

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The general form of a vector i given by the identity:

v = x*i + y*j

We'll use the rule of dot product.

u*v = (5i+2j)(xi + yj)

u*v = 5xi^2 + 5yij + 2xij + 2yj^2

ij = 0 and i^2 = j^2 = 1

u*v = 5x + 2y

We'll get the following system to solve:

5x + 2y = 15 (1)

w*v = (i-j)(xi + yj)

w*v = x - y

x - y = 17 => x = 17 + y (2)

We'll substitute (2) in (1):

5(17 + y) + 2y = 15

Removing the brackets, we'll have:

85 + 5y + 2y = 15

7y = 15 - 85

7y = -70

y = -10

x = 17 - 10

x = 7

Therefore, the requested vector is: v=7*i - 10*j

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