Question 7 Which of the following statements is true? Select...

Question 7 Which of the following statements is true? Select all that apply. The Cartesian unit vectors \hat{x}, \hat{y}, and \hat{z} are the only unit vectors that exist. All unit vectors are unitless. 1 pts To determine a unit vector that describes the direction that a particular vector is pointing, you need to divide the vector by its norm. Unit vectors are the only type of vectors that you can divide by. All unit vectors have a norm of one. Unit vectors are expressed differently than regular vectors by drawing a \"hat\" over their name instead of a regular \"arrow\",

Transcript

00:01 Hello students.

00:03 Here a question is that we have to determine whether the following statements are true or fall.

00:08 If the statement is true we have to explain why it's true and if the statement is false so we have to prove a counter example.

00:17 So here our first statement is that every vector has a norm.

00:22 We know that this is true because if there is a vector the vector have a length and norm in length if let's if we have a vector v and ab is its component then its norm will be equals to under root a square plus b square so this is its now even if we have a zero vector like we have a zero vector in 2 r2 so the norm of this vector will be equals to zero as zero is its norm.

01:04 So we can say that every vector of a no.

01:08 And the next statement is here that given any vector v, there is the unit vector in the direction of v.

01:19 If we have given a vector v, so there is a unit vector in the direction of v, it's true that if we have a vector v, like here, we have its components are 049, okay? so we can say that there this vector can be written as 011.

01:55 We can write it as a node vector, but it is false because here the statement is that any vector there is a node vector in the direction.

02:06 If we have a zero vector like zero vector in two, so we cannot write a vector in the direction of zero -zero so that's why the statement is false it's true for all the vectors except non -zero vectors then the unit vector in the direction of a given non -zero vector v has always shorter than v it's not necessary because if we have a vector like like we have given a vector of 0 and minus 1.

02:50 It's not necessary that there is a vector which is shorter than 0 and minus 1.

02:56 It can be 0 or 1.

03:01 Okay, sorry, this is false.

03:03 And the next statement is that given 2 vector a and b in r3, the vector from a to b is denoted by ab.

03:11 It means that if we have a vector of here, we have a, point in r3 wind a, b and c and we have another point b is a nor, b nor and c nor.

03:27 If we say a vector from a to b, it's mean that the term the initial point of this vector is a and the terminal point is b.

03:36 And to find a vector a, b, we have to subtract the terminal point and the initial point.

03:44 This is a vector from a to b.

03:47 And if they say a vector from a to b, it means that, and if we say a vector from b to a, it's mean that the initial point is b and the terminal point is a.

03:59 And to find this vector, we have to subtract the terminal and the initial...

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