Okay, does it apply also to distance between planes, lines? I mean perpendicular d=shortest d? June 2013, q8 first part the first method used in the mark scheme is really confusing, if someone can explain that, I will be really grateful!
u got the solution for them also for 7c would you use the direction vector of QR and then add the position vector P? seeing as QR seems to be parallel to PS.
Thanks Oh I see, but does this apply for the distance between line and plane or two planes or two lines? Because in the book, they used different methods to find the shortest distance and perpendicular distance between two parallel lines?
nice, interesting question (had to take a peak at the MS and saw they equated the planes lol) but for the last part theyre saying the area of a pyramid is 1/3 (a.bxc)?
Thanks Oh I see, but does this apply for the distance between line and plane or two planes or two lines? Because in the book, they used different methods to find the shortest distance and perpendicular distance between two parallel lines?
The formula is specifically for the distance between a line and a plane.
The distance between two lines is a C4 method.
The distance between two parallel lines is very similar, if not the same now I think about it. Use a specific point on one line, find the general point on the other line, find the vector from the specific point to the general point, then dot product equals 0 for the specific to general and the direction of the lines. Then you should be able to find the distance.
The distance between two planes, well once you've thought about it unless they're perfectly parallel all planes eventually intersect......
And then of course there's that nasty formula you need to remember for the distance between two skew lines
nice, interesting question (had to take a peak at the MS and saw they equated the planes lol) but for the last part theyre saying the area of a pyramid is 1/3 (a.bxc)?
The formula is specifically for the distance between a line and a plane.
The distance between two lines is a C4 method.
The distance between two parallel lines is very similar, if not the same now I think about it. Use a specific point on one line, find the general point on the other line, find the vector from the specific point to the general point, then dot product equals 0 for the specific to general and the direction of the lines. Then you should be able to find the distance.
The distance between two planes, well once you've thought about it unless they're perfectly parallel all planes eventually intersect......
And then of course there's that nasty formula you need to remember for the distance between two skew lines
Really thanks for the detailed explanation! and the dot product is equal to 0 because it's the perpendicular distance(which is the same as the shortest distance) no?
But one thing regarding to the shortest distance and the perpendicular distance, I am still a bit confused because, I know the shortest distance is the same as perpendicular distance when we are talking about the distance from a point to plane/line, But what about when it's regarding to the distance between two planes or a line and a plane, are the perpendicular distances between them the same as the shortest distances between them?
Really thanks for the detailed explanation! and the dot product is equal to 0 because it's the perpendicular distance(which is the same as the shortest distance) no?
But one thing regarding to the shortest distance and the perpendicular distance, I am still a bit confused because, I know the shortest distance is the same as perpendicular distance when we are talking about the distance from a point to plane/line, But what about when it's regarding to the distance between two planes or a line and a plane, are the perpendicular distances between them the same as the shortest distances between them?
Sorry if the question is silly
Honestly I don't have anything in my notes on finding the distance between two planes or a line and a plane. You only need to concern yourself with the distance between a point and a plane/line.
Regarding the distances between two lines, you'll either be asked to find the distance between two parallel lines or two skew ones.
And yes the dot product must equal 0 because cos(90) is 0.
Try visualising a line and the origin, no matter how you draw it, the shortest distance between the line and the origin will always be perpendicular to the line.
just wondering. seeing as it says it must go through P and that the direction vector is the same as the other one QR seeing as they are parallel does this mean i could just say r= position vector of P plus the direction vector QR
nice, interesting question (had to take a peak at the MS and saw they equated the planes lol) but for the last part theyre saying the area of a pyramid is 1/3 (a.bxc)?
Yeah I thought it was pretty cool how they just worked out the line of intersection of both planes.
just wondering. seeing as it says it must go through P and that the direction vector is the same as the other one QR seeing as they are parallel does this mean i could just say r= position vector of P plus the direction vector QR
yeah you can lol but, you only find that out the question after, i also assumed that at first