Find the magnitude ||v||, to the nearest hundredth, and the di...

Question

Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.

v = (7i - 3j) - (10i - 3j)

Accepted Answer

Welcome back, everyone find the magnitude and direction angle of the vector A given below express your answer to one decimal place where given A equals 31 I minus 17 G minus 25 I minus 17 G. And we're given for choices A 6.0 and zero degrees B 6.0 and 90 degrees C 6.0 and 180 degrees and D 36.0 and zero degrees. So first of all, let's notice that the given vector corresponds to the component form and we can isolate two different vectors. We have a difference of two vectors. What we want to do is basically combine the like terms, right? So we're going to take 31 I minus 17 J and we're going to distribute that negative sign. So we are subtracting 25 I and then we are adding 17 J. Now let's combine the like terms. We have 31 I minus 25 I, this gives us six I and then negative 17 G plus 17 G gives us zero J. So our vector A has a form of six I and our component form of the given vector can be written as a XDX component multiplied by I plus the Y component. A Y multiplied by J. Those are unit vectors I and J, right. And in this case, we can say that A X is equal to six, that's the number in front of I A Y is equal to zero. We don't have any Y component. Let's identify the magnitude. We can recall that magnitude of a vector can be expressed as the absolute value of A, it was square root of A X squared plus A Y square. And we can simply substitute the value of A X which is six squared, our A Y zero. And we end up with square root of 36 which is six. And now if we want to report it to one decimal place, that's simply 6.0. Now to identify the magnitude, we first of all want to understand where this factor is. It has a positive A X component and zero for the A Y component. And this means that it's on the X axis between quadron one and four. So our vector will essentially have a zero degree angle because it's on the X axis and it's pointing to the right. But we can also use the formula whenever we are dealing with quadrants one and four, the angle theta can be found as the inverse of 10 of the ratio between A Y and A X. In this case, A Y is equal to zero and A X is equal to six. So we're taking the inverse of 10 of zero, which is equal to zero. So essentially, once again, if we want to add that one decimal place, we can state 0.0 degrees even though it's exactly zero, right? So now looking at the answer choices, we can conclude that the correct answer to this problem corresponds to the answer choice A and that's it. We have solved this problem. Let's eliminate the absolute value for the initial expression, right? Because we have defined our vector. Let's only leave the absolute value for the magnitude part. Thank you for watching.

Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.

v = (7i - 3j) - (10i - 3j)

Key Concepts

Vector Subtraction

Magnitude of a Vector

Direction Angle of a Vector

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