5

Point) Let2 2 ) ,B = (-6 1) c= (} 2A =Then411 412 021 022A + BT =where 411021022andCq C12 C21 C22A - B+ CT =where C11C12C21C22012...

Question

Point) Let2 2 ) ,B = (-6 1) c= (} 2A =Then411 412 021 022A + BT =where 411021022andCq C12 C21 C22A - B+ CT =where C11C12C21C22012

point) Let 2 2 ) ,B = (-6 1) c= (} 2 A = Then 411 412 021 022 A + BT = where 411 021 022 and Cq C12 C21 C22 A - B+ CT = where C11 C12 C21 C22 012



Answers

For the points $A(3,4), B(6,10), C(a+2, b+5)$ and $D(b+4, a-2),$ find the values of $a$ and $b$ such that $\overrightarrow{A B}=\overrightarrow{C D}$

And and it is given there to see is the point online segment A B. That is twice as far be from. Okay. So if this is a line segment A B and C. Is the point. Okay, C. Is the point? Um that is twice as far be as it is from. Mm. So if this is C. Okay, And if this is X, this becomes two x. And given that small is oh, a vector small, B. S O. B victor, and C. Is the victor? Okay. Uh huh. Okay. If this is oh so a vector is a then we will be victorious. B. Okay. And we'll see victories. See selected, going to show that sequel to two or three A plus one by three. B. Yeah. Okay, so if this is like this, so a B victor If A B. S. X. So this is one by three, this is okay. And see victor be returned evicted this, you see. So here, if we write it as a C. Like this, so in the strangle we can write a vector equal to sorry, evicted place X. Vector or vector will be equal to see victor. Similarly here we can right see vector plus expect so I do expect equal to ah be evicted. If we could just eliminate the value of facts, we have to multiply this with two. So this becomes to a vector Plus two Expected equal to to see Victor and see victor place to expect. It will be equal to be evicted. Now subtract minus minus minus this will get cancelled out. So we should right here as to a vector minus c vector equal to to see vector minus b victor. So if we add selected to both, the sides will be getting three C vector equal to be vector plus. Do it victor. So let's divide both sides by three will be getting see victory equal to two by three A vector place one x 3 B victor. This is being written here as a sequel to to buy three a Plus one x 3 B. Since Fruit. Thank you.

In this problem, we are given the coordinates of two points and we need to determine certain victims and their magnitudes. Now, in the first question we need to determine the magnitude of the victor. E. Now the vector oa in component form will be the same as the coordinates of the point. E. So this vector in component form will be minus two minus 63 And does the magnitude of oh a will be equal to the square root of the sum of the squares of the components. So this will be the square root of minus two square plus minus six square plus three square. Now this will be equal to square root over 49 and the value of that is equal to seven. So the magnitude of the vector U. A. is equal to seven. The next problem we have been asked to determine the magnitude of the vector U. B. Now the vector will be in component form will be the same as the coordinates of P. So that will be three minus 4 12. And does the magnitude of the vector ruby will be Square root of three square plus -4 square last 12 square. That is equal to the square root of 169 and the value of that is equal to 13, so the magnitude of obi is 13. And the next problem we have been asked to determine the victor A B. Now that will be obi minus O. A. The position vector of b minus the position vector of a. So that will be three minus for 12 minus minus two minus 63 So we subtract the corresponding components, we have three minus of minus two. So that's three plus two minus four minus minus six. So that's minus four plus six. This will be 12 minus three. So this vector will be 5 to 9 in the next part, we need to determine the magnitude of this victor, Evie. That'll be square root over five square plus two square plus nine square. This is equal to square root over 100 and 10 and the value of that is approximately equal To 10.49. Next we need to determine the victor E. Now this will be minus of the victor A B. So this will be equal to minus of the Victor E. B., which we obtained as 5-9. So this will be -5 -2 -9. And last of all, we need to determine the magnitude of the vector B. A. So that will be the magnitude of minus of a B. Which will be equal to the magnitude of a B. So the magnitude of be, it will be the same as the magnitude of a B. Which we already obtained over here in part B. So the value of this Is approximately equal to 10.49

So here we are, given that B and C are in A that is a BNC are automatic progress. So then we need to find out point through which the given line that is X plus be very plus E siecle zero always passes through. So we need to find that point where the given line passes through this particular point. Okay, so here it is given that a B and c r a p. Therefore we can write it as to be easy colonial policy that is negative. A plus to be minus C is equal to zero or a minus to B plus Easy zero. Therefore X plus B. Right policy will pass through point one comma minus.

In the trenches process upon in to this place here. Simple Anderson. With a Z, we have the thanks. And we have, uh Why, yeah, Why next? And it's see. So the first point Want to plant with being minus 212? So we wanted to have a monster for the X. So we have extended line now and then We have two months to from the exit. So be somewhere here. It's gonna steal for the X one. Follow why and do fa Lizzie. So from here and we're trying to draw, uh, the Tenggara parks, we can draw it up. Yeah, and now isn't Maybe I'm good. Yeah. Yeah, And then we know, You know, I don't think now. Oh, yeah. So the bond we're looking for would be at this point. Now, this will be the minus 21 and two. So similarly, it would just blonde upon to ministry minus one. So have the Jew from the X somewhere here, two months, tree for the y. So much extended. Why? No, I never have That is only minus three and minus one from disease and we need to extend down. Let me minus one on again. And we were trying to draw on the box again, got them in the bunks. And then we were again, uh, Santa. So the bones were little for would be. And this phone now, So it would be, uh, two months, three months, one, and similarly, DuPont three months to do so. We have the excellent about you three. So three somewhere here. Three. And why would u minus two. So I will be here. Wants to and say, Could you chew? And again we need to turn them the rectangular box again. And you have this one now? No, down here. You know it got this one. Don't go, e. It is. So the wrong written form will be And it's prone now. So it's gonna be the three months to and you here. That's the way Would drown the crowd. Do That's the way planted pointing to this place


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