Question

find the vector whose magnitude is 3unit that are prpindecular to both 2i+j+k and i_j_k

Answer 1

Answer:

let the vector be

Ai^+ Bj^+ Ck^

For vectors perpendicular to each other, their dot product is 0

Thus,( Ai^+ Bj^+ Ck^).(2i^+j^+k^)=0

=> 2A+B+C=0 ....(i)

similarly,

( Ai^+ Bj^+ Ck^).(i^-j^-k^)=0

=> A-B-C=0 ...(ii)

adding (i) and (ii)

3A=0 => A=0

Now, √(A^2+B^2+C^2)=3...(iii)

so, putting A=0 in ii and iii,

B+C=0 => B=-C

B^2+ C^2=9

so, (-C)^2 + C^2= 9=> 2C^2=9=> C=3/√2

so, B=-3/√2

Hence, The required vector is

(-3/√2)j^+ (3/√2)k^