IIT JEE , AIEEE Forum - Mathematics , Vectors

karthik_abiram

Q] If a.r =c and (a cross r) =b then r vector is equal to

1] 0 vector

2]ca + (a cross b)

-----------------

/a/²

^3]ca -(a cross b)

^{----------------}

^/a/2

^4]a - (a cross b)

^{-----------------}

^{c /a/2}

^{plzz POST A DETAILED SOLUTION}

rajat

r u sure this is the ryt question ??

i mean

it says a.r = c { all in vectors }

how can "c" be a vector . coz a.r is a scalar . ???

re-chekc

karthik_abiram

sorry...........plz try it now

rajat

ne ways . the answer : 3

i.e

ca - (a cross b)/ a^2

i'll post the soln. soon

rajat

take vector a along the + x-axis . and vector R in the xy plane ,then b is along the z-axis .

R = Rxi + Ryj

Rx = IRIcostheta where theta is the angle between a and R

and Ry = IRIsintheta

using the given condtion , get the value of IRIsintheta and IRIcostheta

also unit vector i = vector a /I a I

and unit vector j = - (a cross b)/I ab I

u'll get it

(just draw the diagram,everything will be crystal clear )

at least give me a salute now ,i have answered all ur vector problems

karthik_abiram

thanx...........plz always post a detailed solution like this..........u will certainly get with out asking ;-)

magiclko

its like this karthik

a. r = c

and a X r = b

taking cross-product with a to both sides of above equation we have

a X (a X r) = a X b

=> (a.r) a - (a.a)r = a X b

=> c a - (|a|^2) r = (a X b)

=> r = ca - (a X b)

|a|^2

btw this is my 800th post