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Vectors (Foundations)

Core skills for this exam family.

Phase 2 · JEE

FoundationsStandardAdvanced

Vectors: core idea

∣v⃗∣=x2+y2|\vec v|=\sqrt{x^2+y^2}.

Example problem: hint and answer

Magnitude of ⟨3,4⟩\langle3,4\rangle?

Hint: Pythagorean. Answer: 5.

Practice (9 problems — type your answers)

  • 1. ⟨1,2⟩+⟨3,4⟩\langle1,2\rangle+\langle3,4\rangle: first component?

  • 2. ⟨1,0⟩⋅⟨0,1⟩\langle1,0\rangle\cdot\langle0,1\rangle?

  • 3. Unit vector along ⟨0,5⟩\langle0,5\rangle: yy-component?

  • 4. ⟨2,3⟩−⟨1,1⟩\langle2,3\rangle-\langle1,1\rangle: second component?

  • 5. ⟨1,2⟩⋅⟨1,2⟩\langle1,2\rangle\cdot\langle1,2\rangle?

  • 6. i×j\mathbf i\times\mathbf j: zz-component of result?

  • 7. Angle between ⟨1,0⟩\langle1,0\rangle and ⟨0,1⟩\langle0,1\rangle in degrees?

  • 8. Projection of ⟨3,4⟩\langle3,4\rangle onto ⟨1,0⟩\langle1,0\rangle: magnitude?

  • 9. ∣⟨0,0,5⟩∣|\langle0,0,5\rangle|?

Vectors Practice Problems — Foundations