Question

If vector X is a unit vector such that
( vector X ) cross product( I cap ) = K
FIND
( vector X ) dot product( J cap )
{CAP MEANS ^ }

Answer 1

$$\begin{gathered} \overrightarrow{\mathrm{x}}\times \hat{\mathrm{i}}=\mathrm{K} \\ \left|\overrightarrow{\mathrm{x}}\right|\left|\hat{\mathrm{i}}\right|\mathrm{sin\theta }\hat{\mathrm{n}}=\mathrm{K} \\ 1\times 1\mathrm{sin\theta }\hat{\mathrm{n}}=\mathrm{K} \\ \mathrm{sin\theta }=\frac{\mathrm{K}}{\hat{\mathrm{n}}}....\left(1\right) \\ \mathrm{Now}\overrightarrow{\mathrm{x}}.\hat{\mathrm{i}}=\left|\overrightarrow{\mathrm{x}}\right|\left|\hat{\mathrm{i}}\right|\mathrm{cos\theta } \\ =1\times 1\times \sqrt{1-{\sin }^2\mathrm{\theta }} \\ =\sqrt{1-{\left(\frac{\mathrm{K}}{\hat{\mathrm{n}}}\right)}^2} \end{gathered}$$