If u = < -7, 6> and v = < -4, 17> , which vector can be added to u + 3v to get the unit vector < 1, 0> as the resultant vector? a. w = < 18, -57> b. w = < 18, -45> c. w = < 20, -57> d. w = < 20, -45>

The value of the vector w is <20, -57>.

Whenever we add two vectors such that and , we add the corresponding component of one vector to the corresponding component of another vector, and the result vector is known as the resultant vector.

Therefore,

Whenever we multiply a vector such as <x, y> with a whole number a, then each component of the vector is multiplied by the whole number. therefore,

Given to us,

u = <-7, 6>,

v = <-4, 17>,

resultant, R =  <1, 0>

We can write it as,

substituting the values,

Hence, the value of the vector w is <20, -57>.

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none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.