Questions: Find the unit vector u with the same direction as t = -7 i + 10 j + k. Simplify any radicals.
u = □ i + □ j + □ k
Transcript text: Find the unit vector $\mathbf{u}$ with the same direction as $\mathbf{t}=-7 \mathbf{i}+10 \mathbf{j}+\mathbf{k}$.
Simplify any radicals.
\[
\mathbf{u}=\square \mathbf{i}+\square \mathbf{j}+\square \mathbf{k}
\]
Solution
Solution Steps
Step 1: Find the Magnitude of t
Calculate the magnitude of the vector t=−7i+10j+k using the formula for the magnitude of a vector:
∥t∥=(−7)2+102+12
∥t∥=49+100+1
∥t∥=150
∥t∥=25×6=56
Step 2: Divide Each Component by the Magnitude
To find the unit vector u, divide each component of t by its magnitude ∥t∥: