Which of the following is not true about vectors → A , → B ~and → C...

Dot/Scalar product of two vectors gives scalar result. Cross/Vector product will give vector result.

Case:& \left(\overset{→}{A} \cdot \overset{→}{A}\right) \left(\overset{→}{B} \cdot \overset{→}{C}\right)

Both left & right part will be a scalar value and hence its product will also be a scalar value.

Case:~\left(\overset{→}{A} \times \overset{→}{B}\right) \cdot \left(\overset{→}{B} \times \overset{→}{C}\right)

Both left and right part will be a vector, and then these two vectors will undergo dot product and the result will be a scalar value.

Case:~\left(\overset{→}{A} \times \overset{→}{C}\right) \times \left(\overset{→}{B} \times \overset{→}{C}\right)

Both left and right part will be a vector, and then these two vectors will undergo cross product and the result will be a vector~value.

Case:~$\overset{→}{A}$\times \left(\overset{→}{B} \times \overset{→}{C}\right)

Both left and right part will be a vector, and then these two vectors will undergo cross product and the result will be a vector value.