The value of the constant p such that the vectors 2i^−j^+k^,i^+2j^−3k^  and 3i^+pj^+5k^  are coplanar is:

For the three coplanar vector a→,b→  and c→ , their scalar tripe product a→.(b→×c→)  must be zero.Here a→.(b→×c→)=|ax   ay   azbx    by    bzcx    cy    cz|=| 2    −1         1  1        2    −3  3         p       5 |=2(10+3p)+1(5+9)+1(p−6)⇒28+7p=0Or p=−4