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01010.0 pointsThe matrices I2 #[6 9 Jz = J[4 %] are perpendicular and have unit length with respect to the Standard Inner Product on R2*2 True or False?1. True2.0...

Question

01010.0 pointsThe matrices I2 #[6 9 Jz = J[4 %] are perpendicular and have unit length with respect to the Standard Inner Product on R2*2 True or False?1. True2.0 False, they don t have unit length_3. False, they aren t perpendicular.

010 10.0 points The matrices I2 #[6 9 Jz = J[4 %] are perpendicular and have unit length with respect to the Standard Inner Product on R2*2 True or False? 1. True 2.0 False, they don t have unit length_ 3. False, they aren t perpendicular.



Answers

Determine whether each statement is true or false. If the dot product of two nonzero vectors is equal to zero, then the vectors must be perpendicular.

This is a simple problem. They gave us two vectors. One is to i minus three J. And the other is six. I plus four J. And they simply ask if those are particular. Well if they're perpendicular then the dot product between them should be zero. Because remember the yeah co sign or the angle between them is their magnitudes. Sorry there. That product of them Fight Imbibes divided by the magnitude of each one. And so we need that to be zero for them. For this is zero then data equals no sorry we want them to be. Yeah if they if they if they need zero then then then if of course annotated zero. Them thing is pi over two or three pi over two or any integer multiple. But Either way that means that there's a 90° angle between them So that's 90°. The ankle between them, There's 90° or 270°. And so we all we need to do is then check is this thing zero. And so we take the dot product, we get 12 And then -12, and so that is zero. So they are indeed orthogonal to each other but are perpendicular to one another. And again, all we need to do is check the dot product and make sure that that zero.

The questions is the two vectors U equals zero common zero on V equals minus 12. Former six when U and V are part the land. Now this statement is true because the victor zero is 4 to 1. Every other victor does. This statement is true.

Okay, This question asks us if orthogonal vector's have a dot product of zero. So let's say we have two factors here give you and the and their orthogonal. So we know that you Davi is equal to the magnitude of you times the magnitude of the times, the co sine of the angle between them And in our case, our angle is 90 degrees. Since these two vectors, air perpendicular and co sign of 90 is zero. So orthogonal Vector's do indeed has dot product equal to zero.

The young question you re in the blue are non Jews or directors, so we have to prove that we plus that list nautical, Sajida. Uh, let's assume we can find the magnitude off we plus w actor. So it is a questo mod off the square, less modoff w square plus toe. We got the blue right. This formula, you know, it is given that we dot ws request to Jesus because it is also one. So this becomes Jesus. Uh, and they bought the V and w are non directors, so we can see that we plus W is request toe. Since these two are non zero, so we can see that we can say that this is not equals to zero as the given a statement is correct.


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