A-Level Further Maths F3-07 Scalar Product: Re-Introducing the Cartesian Equation of a Plane

[@alihamzakhan9521]

i was in shock when i actually understood how this all related back to the plane equation. Genius

[@GCSEALevelMaths2025]

I like this new camera may I ask what it is? It looks super clear.

[@TLMaths]

I went with this one in the end: www.currys.co.uk/gbuk/cameras-and-camcorders/digital-cameras/compact-and-bridge-cameras/canon-powershot-sx620-hs-superzoom-compact-camera-black-10161431-pdt.html

[@Echo-zp5ll]

so helpful, thanks

[@gopalgeorge3632]

Hi I asked this question and forget the answer sorry and I can't find the original comment where I asked, what should I remember/get familiar with for the AQA large data set?

[@TLMaths]

I made this video on it: ua-cam.com/video/-3Shq9HDIOo/v-deo.html

[@dillon_1944]

i was told d is equal to a dot n, not -a dot n

[@TLMaths]

Depends if you write n_1x + n_2y + n_3z + d = 0 (as I did in the video), or n_1x + n_2y + n_3z = d

[@Tom-hp4bq]

@@TLMaths Which do you use for calculating the distance from a point to a plane? a.n=d or -a.n=d

[@TLMaths]

​@@Tom-hp4bq The distance from (p,q,r) to the plane ax+by+cz+d=0 is |ap+bq+cr+d|/sqrt(a^2+b^2+c^2)

[@Tom-hp4bq]

@@TLMaths
Should you use:
ax+by+cz+d=0 (-a.n=d)
and
ax+by+cz=d (a.n=d) ?
With these two equations d can either be positive or negative, which do you use when calculating the distance from a point to a plane? Sorry I'm just quite confused

[@TLMaths]

@@Tom-hp4bq You just need to rearrange ax+by+cz=d into the form ax+by+cz+d=0 by subtracting d from both sides, then you can use:
The distance from (p,q,r) to the plane ax+by+cz+d=0 is |ap+bq+cr+d|/sqrt(a^2+b^2+c^2)