You may let OB or OC to be the position vector of the fixed point on the line. For part 8b, your parameters values will be different from mine, due to different fixen point used in forming the line equation. But anyway, it will not affect the position vector of the intersection point
Integrate 1/(x^2+3^2) dx= (1/3)tan^(-1)(x/3). If you factorise 3 in the numerator, then the integration is 3* (1/3)tan^(-1)(x/3)=tan^(-1)(x/3). It's the same answer as my presentation in the video
From part b, zw= 3+3 (square root 3) + (-3+3(square root 3)i. When you look at the right hand side of part d, the division is the imaginary part of zw divided by the real part of zw.
Refer to the right side of the equation, that is the division of the imaginary part and the real part of zw. Therefore, the left side, arg(zw) =arg(z) +arg(w)
Please visit my YT Channel and go to the PLAYLIST in the Content folder -CAIE Pure Math 3. You may find the video there, and also past years P3 videos.
The general vector equation of a line is r=a+tb, where a is the position vector of a point on the line and b is the direction vector the line. Since the line passes through BC, therefore the direction vector is vector BC, but vector BC=(3 3 -3)=3(1 1 - 1). So the simplest form of the director vector, b=(1 1 - 1) in the general vector equation is the line
Yes, you may put it that form. But, vector equation of the line is r=a +tb. tb means parallel vector, hence I will just write b in the simplest form by factoring the common multiple, i.e. 3
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Very helpful videos.
For the iteration am getting a final answer of 0.727
Does the answer vary with different calculator
Because i press the same as you but confused for not getting the same answer
Did you calculate in radians?
No
cos 3(0.75) and cos(3x0.75) when u type in calculator is totally diff ans. That why u get 0.727
Thanks
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teacher... in question 8a i used for my L1 OC instead of OB and i couldn't get the coordinates in 8b ...does it matter which one we choose?
You may let OB or OC to be the position vector of the fixed point on the line. For part 8b, your parameters values will be different from mine, due to different fixen point used in forming the line equation. But anyway, it will not affect the position vector of the intersection point
For integration to obtain tan inverse in 10b why do we not multiply the tan inverse (x/a) by 1/3 as the integration has 3 as its numerator
Integrate 1/(x^2+3^2) dx= (1/3)tan^(-1)(x/3). If you factorise 3 in the numerator, then the integration is 3* (1/3)tan^(-1)(x/3)=tan^(-1)(x/3). It's the same answer as my presentation in the video
1:28:10 can you please explain for qu 9part (d), am not understanding how and why should arg (zw) be used to answer
From part b, zw= 3+3 (square root 3) + (-3+3(square root 3)i. When you look at the right hand side of part d, the division is the imaginary part of zw divided by the real part of zw.
@@MathWorld-yp9odya how should we know that we must use this please
Refer to the right side of the equation, that is the division of the imaginary part and the real part of zw. Therefore, the left side, arg(zw) =arg(z) +arg(w)
hii for question 8a why cant we put 333 instead we put direction vector? i dont get it
The direction vector, b, is parallel to the vector BC, BC=(3 3 - 3)=3(1 1 - 1). Hence, b=(1 1 - 1)
@@MathWorld-yp9od oh so we must always take out common multiple for direction vector then ?
Yes, to get the simplest form of the direction vectot
Can you do paper 31 for may2024
Please visit my YT Channel and go to the PLAYLIST in the Content folder -CAIE Pure Math 3. You may find the video there, and also past years P3 videos.
Hi, I don't understand how b is parallel to BC @53:34
The general vector equation of a line is r=a+tb, where a is the position vector of a point on the line and b is the direction vector the line. Since the line passes through BC, therefore the direction vector is vector BC, but vector BC=(3 3 -3)=3(1 1 - 1). So the simplest form of the director vector, b=(1 1 - 1) in the general vector equation is the line
@@MathWorld-yp9od so if we put 3 3 -3 , it will also give correct answer right?
Yes, you may put it that form. But, vector equation of the line is r=a +tb. tb means parallel vector, hence I will just write b in the simplest form by factoring the common multiple, i.e. 3