A few problems on tensor calculus which i could not solve.

1.if $A_{ij}$ is a skew-symmetric tensor,then show that $(B^i_jB^k_p+B^i_pB^k_j)A_{ik}$=0.

2.if the relation $a_{ij}u^iu^j=0$ holds for all vectors $u^i$ such that $u^ip_i$ where $p_i$ is a given covariant vector ,then $a_ij+a_ji=p_iv_j+p_jv_i$ where $v_j$ is some covariant vector.

3.if the equality $a^i_ju_i=Ku_j$ holds for any covariant vector $u_i$ such that $u_iv^i=0$ where $v^i$ is a given contravariant vector, show that $a^i_j=K\delta^{i}_{j} +p_jv^i$

how can i solve these problems

-