What can be the unit vector of a plane to which a perpendicular dropped from origin(o) meet at A(1, 4, 6)?
What can be the unit vector of a plane to which a perpendicular dropped from origin(o) meet at A(1, 4, 6)?
The correct options are
A
C
The line OA which is perpendicular to the area can easily be made a vector because if you notice it is actually the position vector of point A which lies on the are element.
Question does not demand any reference to the magnitude of area and hence, you don’t have not to other about it.
Mathematically,
→OA=^i−4^j+6^k
Now you can easily calculate its unit vector if you know, →A=→|A|^A for any vector
^OA=^i+4^j+6^k√(1+16+36)=^i+4^j+6^k√(53)
now if →OA is ⊥r to the plane, then →AO will also be ⊥rto it.
Hence −^i−4^j−6^k√53 can also be a unit vector perpendicular to the given plane.
Now if we have assigned, →|ΔS|=length of arrow
= 5 units
As clearly shown, surface ΔS lying on a x – z plane can have 2 possible normal’s 1r to it, one towards +y and the other one pointing – y.
Learning: Both directions will lie along the same axis but facing away. Mathematically it implies that both vectors will have opposite signs.
e.g. ^B=−^A
A
C
The line OA which is perpendicular to the area can easily be made a vector because if you notice it is actually the position vector of point A which lies on the are element.
Question does not demand any reference to the magnitude of area and hence, you don’t have not to other about it.
Mathematically,
→OA=^i−4^j+6^k
Now you can easily calculate its unit vector if you know, →A=→|A|^A for any vector
^OA=^i+4^j+6^k√(1+16+36)=^i+4^j+6^k√(53)
now if →OA is ⊥r to the plane, then →AO will also be ⊥rto it.
Hence −^i−4^j−6^k√53 can also be a unit vector perpendicular to the given plane.
Now if we have assigned, →|ΔS|=length of arrow
= 5 units
As clearly shown, surface ΔS lying on a x – z plane can have 2 possible normal’s 1r to it, one towards +y and the other one pointing – y.
Learning: Both directions will lie along the same axis but facing away. Mathematically it implies that both vectors will have opposite signs.
e.g. ^B=−^A
