|=0 ⇒3a+b−5c=0⋅⋅⋅⋅⋅⋅⋅(i) ⇒a⟂(i+j+3k)⇒a⋅(i+j+3k)=0 a+b+3c=0⋅⋅⋅⋅⋅⋅⋅(ii) Projection of a on b is 3√6 .
a⋅b
|b|
=3√6
a+2b+c
√1+4+1
=3√6 a+2b+c=18⋅⋅⋅⋅⋅⋅⋅(iii) On subtracting Eq. (ii) from Eq. (i), . 2a−8c=0⇒a=4c⋅⋅⋅⋅⋅⋅⋅(iv) On multiplying 2 in Eq. (ii) and subtracting Eq. (iii), we get a+5c=−18⋅⋅⋅⋅⋅⋅⋅(v) From Eqs. (iv) and (v), c=−2 and a=−8 On putting in Eq. (iii), b=14 a=−8