Let a = i +2 j +λ k, b =3 i -5 j -λ k, a · c =7,2 b · c +43=0, a × c = b × c. Then | a · b | is equal to

Let $\displaystyle \vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $\displaystyle |\vec{a} \cdot \vec{b}|$ is equal to