Let a→=i^+2j^−k^, b→=i^−j^ andc→=i^−j^−k^ be three given vectors. If r→  is a vector such that r→×a→=c→×a→ and r→.b→=0, then r→. a→  is equal to

The given vectors are a→=i^+2j^−k^, b→=i^−j^ andc→=i^−j^−k^ Given r¯×a¯=c¯×a¯ and r¯.b¯=0 ⇒             r¯−c¯×a¯=0⇒r¯−c¯ is parallel to a¯⇒r¯−c¯=ta¯hence,  r=c¯+ta¯r¯⋅b¯=0c¯+ta¯⋅b¯=0t=−c¯⋅b¯a¯⋅b¯=−2−1=2Hence, r¯.a¯=2i+2j+k2=26=12