Question

Let v = (1,-3) and w = (-2,6). Which of the following is true? Check all that apply.

Answer 1

Answer:  The correct options are

(B). The y-component of w is 6.

(D). w = -2v.

Step-by-step explanation:  Given that

$v=(1,-3),\\\\w=(-2,6).$

We are to select all the correct statements from the given options.

The first component in an ordered pair is called the x-component and the second component is called the y-component.

Option (A) is

"The x-component of v is -2".

This statement is incorrect because the first component (x-component) of 'v' is 1.

Option (B) is

"The y-component of w is 6."

This statement is correct, because the second component (y-component) of 'w' is 6.

Option (C) is

"v+w = 36".

Since the sum of two ordered pairs is again an ordered pair, so this option is not correct.

In fact,

$v+w=(1,-3)+(-2,6)=(1-2,-3+6)=(-1,3)\neq 36.$

Option (D) is

"w = -2v".

We have

$w=(-2,6)=-2(1,-3)=-2v.$

So, this option is correct.

Thus, the correct options are (B) and (D).

Answer 2

A) Vectors are usually given in the form (x , y), therefore the x-component of v is 1.

B) Similarly to point A), the y-component of w is 6

C) the magnitude of the vector v+w is given by:
√[(x₁ + x₂)² + (y₁ + y₂)²] = √[(1 + (-2))² + (-3 + 6)²] = √(1 + 9) =√10

D) Compute -2 · v = (-2·1 , -2·(-3)) = (-2 , 6) = w

Therefore options B) and D) are true.