Find the magnitude of the vector $\mathbf{u}=3\mathbf{i}-4\mathbf{j}+12\mathbf{k}$.

Step-by-step solution

1. Write the components of $\mathbf{u}$ as $(3,,-4,,12)$.
2. Square each component: $3^2=9$, $(-4{)}^2=16$, $12^2=144$.
3. Add the squares: $9+16+144=169$.
4. Take the square root of the sum: $\sqrt{169}=13$.
5. Thus the magnitude $|\mathbf{u}|=13$.

Concept tested: Vector magnitude

Published 31 August 2026 · Last updated 16 September 2026 · How this solution was prepared and checked

Related questions

• 1 Find the vector projection of b onto a where a=2i+3j-k and b=-i+4j+2k.
• 2 Given a=2i+3j-k and b=-i+4j+2k, find the angle between them in degrees (nearest integer).
• 3 Find the equation of the plane that passes through P(2,-1,3) and is perpendicular to the line x-14=(y+2)/-2=(z-0)/5.
• 4 Which of the following is the equation of the plane that passes through the point (1,2,3) and has normal vector ⟨ 4,-1,2⟩?
• 5 For the system x+2y-z=3, 2x+4y-2z=6, 3x+6y-5z=2, find the rank of the coefficient matrix and the augmented matrix and state whether the system is consistent. If it is consistent, give the solution.
• 6 Find the minimum and maximum values of the function f(x)=x^2-4x+5 on the interval [1,4].