Let a and b denote 2 2d vectors

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In summary: Hint: If ##a \le b## then ##a^2 \le b^2##In summary, the conversation involved solving a problem in which the goal was to show that a dot product of two 2D vectors, a and b, is less than or equal to the product of their magnitudes. The conversation walked through finding the dot product and magnitude of a and b, and then manipulating the inequality to prove its truth. The final step involved using the property that if a is less than or equal to b, then a squared is also less than or equal to b squared.
  • #36
First, the things you are squaring aren't the same as the things you are multiplying by two, and secondly, (1/2)2 < 2*(1/2) so the basic logic there doesn't work.

You need to do some algebra to re-write the right hand side.
 
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  • #37
Squaring ##1## isn't bigger than multiplying it by ##2##. Look, you need to do some algebraic manipulation with that expression to make it obvious that is is ##\ge 0##. We have led you by the hand to this point and I don't see how we can give you that last step without having worked the whole problem for you.

As a matter of curiosity, what course are you in and what courses have you already had?
 
  • #38
i was thinking the algebra might include taking out common terms but there are none, can i get a hint as to what needs to happen
 
  • #39
LCKurtz said:
We have led you by the hand to this point and I don't see how we can give you that last step without having worked the whole problem for you.
That's how I feel as well.
 
<h2>1. What is the difference between a and b?</h2><p>Vector a and b are both 2d vectors, meaning they have two dimensions: x and y. The difference between them is the value of each dimension. For example, if a = [1,2] and b = [3,4], then the difference between a and b is [2,2].</p><h2>2. How do you add two 2d vectors?</h2><p>To add two 2d vectors, you simply add the corresponding dimensions. For example, if a = [1,2] and b = [3,4], then a + b = [1+3, 2+4] = [4,6].</p><h2>3. Can you subtract two 2d vectors?</h2><p>Yes, you can subtract two 2d vectors by subtracting the corresponding dimensions. For example, if a = [1,2] and b = [3,4], then a - b = [1-3, 2-4] = [-2,-2].</p><h2>4. What is the dot product of a and b?</h2><p>The dot product of two 2d vectors is the sum of the products of their corresponding dimensions. In other words, a · b = (a<sub>x</sub> * b<sub>x</sub>) + (a<sub>y</sub> * b<sub>y</sub>). For example, if a = [1,2] and b = [3,4], then a · b = (1*3) + (2*4) = 11.</p><h2>5. How do you find the magnitude of a 2d vector?</h2><p>The magnitude, or length, of a 2d vector can be found using the Pythagorean theorem: ||a|| = √(a<sub>x</sub><sup>2</sup> + a<sub>y</sub><sup>2</sup>). For example, if a = [3,4], then ||a|| = √(3<sup>2</sup> + 4<sup>2</sup>) = 5.</p>

1. What is the difference between a and b?

Vector a and b are both 2d vectors, meaning they have two dimensions: x and y. The difference between them is the value of each dimension. For example, if a = [1,2] and b = [3,4], then the difference between a and b is [2,2].

2. How do you add two 2d vectors?

To add two 2d vectors, you simply add the corresponding dimensions. For example, if a = [1,2] and b = [3,4], then a + b = [1+3, 2+4] = [4,6].

3. Can you subtract two 2d vectors?

Yes, you can subtract two 2d vectors by subtracting the corresponding dimensions. For example, if a = [1,2] and b = [3,4], then a - b = [1-3, 2-4] = [-2,-2].

4. What is the dot product of a and b?

The dot product of two 2d vectors is the sum of the products of their corresponding dimensions. In other words, a · b = (ax * bx) + (ay * by). For example, if a = [1,2] and b = [3,4], then a · b = (1*3) + (2*4) = 11.

5. How do you find the magnitude of a 2d vector?

The magnitude, or length, of a 2d vector can be found using the Pythagorean theorem: ||a|| = √(ax2 + ay2). For example, if a = [3,4], then ||a|| = √(32 + 42) = 5.

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