This question asks about finding unit vector(a 1 ,a 2 ,a 3 ) such that the equat

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This question asks about finding unit vector(a1,a2,a3) such that the equationisa12+a22+a32=1and the equation of the 0yz plane is 1times x = 0... the unitvector is parallel to the plane so then a1=0 also...that's all I could actually get!
the site has a solution but I do not understand it! Thanks This question asks about finding unit vector(a1,a2,a3) such that the equationisa12+a22+a32=1and the equation of the 0yz plane is 1times x = 0... the unitvector is parallel to the plane so then a1=0 also...that's all I could actually get!
the site has a solution but I do not understand it! Thanks

Explanation / Answer

QuestionDetails: This question asks about finding unit vector(a1,a2,a3) such that the equationisa12+a22+a32=1
and the equation of the 0yz plane is 1times x = 0... the unitvector is parallel to the plane so
then a1=0 also... that's all I could actuallyget!
the site has a solution but I do not understand it! Thanks
IS IT THE QUESTION THAT YOU HAVE TO FIND A UNIT VECTOR(a1,a2,a3)
WHICH IS PARALLEL TO OYZ PLANE ?ASSUMING SO
NORMAL TO PLANE OYZ IS X AXIS ..THAT IS EQN. IS Y=0 AND Z=0 IN3D.
THAT IS ITS DIRECTION RATIOS ARE [P,0,0] OR SIMPLY [1,0,0]
SO IF YOU WANT A UNIT VECTOR [A1,A2,A3] PARALLEL YO OYZ PLANE ,
THEN IT WILL BE PERPENDICULAR TO THE ABOVE NORMAL WITH DRS OF[1,0,0]
SO WE SHOULD HAVE
A1*1+A2*0+A3*0=0
A1=0
SO WE GET THE VECTOR AS
[0,A2,A3]
BUT FOR IT TO BE UNIT VECTOR WE SHOULD HAVE
(A2)2+(A3)2=1......SO WE CAN SAY THE VECTORIS
[0,SIN(T),COS(T)] WHERE T IS ANY REAL NUMBER SINCE WE ALWAYSHAVE
SIN2(T)+COS2(T)=1
HENCE THE REQUIRED UNIT VECTOR IS [0,SIN(T),COS(T)]

ALTERNATELY IF YOUR REQUIREMENT IS THAT [A1,A2,A3] SHALL BE
PERPENDICULAR TO OYZ PLANE , THEN BY THE SAME METHOD WE GET
THE ANSWER AS [1,0,0]...
PLEASE CHECK UP YOUR REQUIREMENT OF THE UNITVECTOR.

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