Write the distributive law for the product of two vectors.
Define the scalar product of two vectors.
If the projection of $2 \hat{i}+4 \hat{j}-2 \hat{k}$ on $\hat{i}+2 \hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be.
Force $F$ applied on a body is written as $F =(\hat{ n } \cdot F ) \hat{ n }+ G$, where $\hat{ n }$ is a unit vector. The vector $G$ is equal to