Question

Projection of 2$\hat i$+4$\hat j$−2$\hat k$ on $\hat i$+2$\hat j$−α$\hat k$ is zero. Then, the value of α will be________.

Answer 1

The projection of one vector will be zero on another vector only when they are perpendicular to each other
Let the two vectors be $\vec A$=2$\hat i$+4$\hat j$−2$\hat k$ $\vec B$=$\hat i$+2$\hat j$+α$\hat k$
$\vec A$⋅$\vec B$=0 as A→should be perpendicular to $\vec B$
⇒2+8−2α=0
⇒α=5