Direction Cosines & Direction Ratios of a line in 3-D space | CBSE 12 Maths NCERT Ex 11.1 intro

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[@bhargabborah4194]

Direction ratio = difference of the coordinate (x2-x1) Direction cosine = a/root (a²+b²+c²)

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guru ji aapki intro vdo dekhne ke baad exercise aasani se ho jaati hai

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[@bey0u414]

for the vectors, there will be infinite sets of direction raitos .That is because a line has magnitude it can have infinite direction ratios both negative and positive .But in vectors ,direction cosines will be only positive or only negative .so it will still have infinite direction ratio of only one sign.

[@MohitBaboria]

How? A vector has only one set of direction ratios Because it has a mixed magnitude so it mean it has a terminal point and initial point and it's direction ratios can be obtained by subtracting the corresponding coordinates initial point from the terminal point

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Sir , kya ek normal line mein bhi free vectors jaisa property hota hai???

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Sir last wala part ni aaya, D.C. of line || to x-axis does not touching y-axis neither z-axis or touching either one of them, so how that line making 90° with y and z axis. 🤔🤔 (agar line x axis ke parallel hogi to wo line sirf y axis ko touch kregi ya phir z axis ko touch kregi ya phir kisi ko bhi touch nhi kregi. to phir aapka answer (1,0,0) kaise aaya??) same case for other axis smjh me aaya na sir jo mene btaya??

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[@shubhampal0442]

Direction cosines for a vector are unique but it may have infinite direction ratios

[@ashiramavat6555]

Yes

[@mathsismylife6192]

Can you refer any book mentioning this . I have been searching for that for years. no one pointed any so far But I believe lines have infinite direction ratios but when we increase or decrease the length of a vector we are getting different vectors so Direction Ratio is unique in the case of vectors

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[@raghumalhotra3490]

Sir direction ratio of vector is also x2-x1...and we can take infinite set of x2 and coresponding x1 on vector as welll..so vector must also have infinite set of direction ratios ..plz reply

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Sir we measure angles in anticlockwise direction. But when you measure π-alpha beta or gamma. You have taken in clockwise direction

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[@d2abhishekkumarverma854]

Hello sir Direction ratio for a line is infinite but for vector it is unique Is it correct sir

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Yes

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[@niranjan3267]

Sir let a line make an angle 60 degree with all axis then it's dcs will be < cos(60), cos(60),cos(60) >. But it not satisfy the condition that l^2+m^2+n^2 = 1, why sir ???

[@smritisamikshyamishra5988]

Direaction ratios for a vector is unique.... am i correct sir.??? Plz reply.

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[@brutalbeast9263]

yes sir ek vector ke bhi infinity Direction ratios hoskta ha kyu if we take a example let i+j+k will be a one vector then Direction ratios=1,1,1 and Direction cosine=1/root3 ,1/root3 ,1/root3 .... and if we multiply this vector by 2 it become 2i+2j+2k vector so direction ratios are 2,2,2 and direction cosine =1/root3 ,1/root3 ,1/root3 ... therefore we have two equal vector and there direction cosine are same and there k(rotio of a/l) also same.. hence prove... and sir i want to thnx you because you i score 93.5 percentile in jee main 2019 jan... thnx alot sir keep doing sir

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[@shaikhumer662]

At 31 :58 answer: yes a vector also have a infinite number of direction ratio If Im wrong please correct me

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Direction cosins for a vector may have infinite direction rations ?? M I right ?? 🙄

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direction ratio of vector can be positively infinite...plz reply??? Am I correct..sir Plz.. :)

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yes, there can be infinite sets of direction ratios of a vector fav dialogue: CHECK KARLO!😁

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how

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[@maalinihema_]

sry sir. i dint get the concept. in order to find the D.C OF LINE PQ, whats the need to draw an other vector RS?! PLZ SOLVE. IS the DC OF PQ NAND RS THE SAME?!!

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prayas kumar have you done NDA*

[@aryushijha4642]

31:50 answer yeh hai Kya sir ki ek line jo vector form me hai uske infinite direction ratios nahi honge kyunki vector ki to ek hi particular direction hoti hai

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Dwi jib gomunotori gosamkyo

[@raghumalhotra3490]

Par jo line hai not vecto vo bhi toh line joining two fixed points hai..and agar line ki direction change kare toh voh a b fixed points se passs nahi kare gi.. also agar line ki direction chage hoti to angle bhi toh change hoga..so non scaler line ki bhi hamne direction change nai ki still it has infinitely many direction ratios and cosines...ao i think ki vector k bhi infinit ho sakte hai..what do you think?

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sir i have a dought that why direction cosines of x axis and line parallel to x axis is (1,0,0) not (+-1,0,0) similarly for yand z axis an lines parallel to it?

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sir, I don't understand how the base's length is (x2-x1)?

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NCERT book ke alawa kaun si book 3D ke liye padhen ? Rahul Rohtak

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3d diagrams are mind-blowing

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Blessed I found this channel today.❤