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Q.
If a vector $2 \hat{i}+4 \hat{j}+6 \hat{k}$ is perpendicular to the vector $5 \hat{i}+6 \hat{j}-a \hat{k}$. Then the value of a is:
Motion in a Plane
Solution:
When the vectors are perpendicular to each other then their dot product is equal to zero
$(2 \hat{ i }+4 \hat{ j }+6 \hat{ k }) \cdot(5 \hat{ i }+6 \hat{ j }- a \hat{ k })=0$
$10+24-6 a =0$
$34=6 a$
$a =\frac{17}{3}$