Scalars, vectors and position vectors sheet3-mark answer frameFind the position vector of P(2, 3, −6) and its magnitude. Write the vector PO⃗ and show that |PO⃗| = |OP⃗|.
How to lay out the answer. Follow the frame, then write it in your own words.
- 1 · Write what is given and what is to be found. Given: P(2, 3, −6), O the origin. To find: OP⃗, |OP⃗|, PO⃗ and |PO⃗|.
- 2 · Write the formula. OP⃗ = xî + yĵ + zk̂ and |OP⃗| = √(x² + y² + z²). PO⃗ = −OP⃗.
- 3 · Write the position vector. OP⃗ = 2î + 3ĵ − 6k̂
- 4 · Find its magnitude. |OP⃗| = √(4 + 9 + 36) = √49 = 7
- 5 · Write the negative and its magnitude.
- PO⃗ = −OP⃗ = −2î − 3ĵ + 6k̂
- |PO⃗| = √(4 + 9 + 36) = 7
- 6 · Check and box the answer. OP⃗ = 2î + 3ĵ − 6k̂, PO⃗ = −2î − 3ĵ + 6k̂, and |OP⃗| = |PO⃗| = 7 units.
Scoring tip: Write the square of each component inside the root. Writing √(4 + 9 + 36) shows the method even if you slip later.
