Exercise · ZW-ORTHOGONAL-VECTORS-006 · ★★☆ Intermediate
If \(u\) and \(v\) are orthogonal, \(\|u\|=3\) and \(\|v\|=4\), what is \(\|u+v\|\)?
Choose one option.
Show answer
- C. \(5\)
Explanation
By Pythagoras, \(\|u+v\|^2=\|u\|^2+\|v\|^2=9+16=25\), so \(\|u+v\|=5\). Adding the norms (7) is the typical mistake.
Review the concept: Orthogonal vectors
Two vectors of \(\mathbb{R}^n\) are orthogonal when their dot product is zero; geometrically, they are perpendicular.
\[u\perp v\iff u\cdot v=0\]
More practice problems: orthogonal vectors
- ZW-ORTHOGONAL-VECTORS-001 Which of the following pairs of vectors is orthogonal?
- ZW-ORTHOGONAL-VECTORS-002 For which value of k are (k,3) and (2,-4) orthogonal?
- ZW-ORTHOGONAL-VECTORS-003 Find k so that (1,k,2) and (3,-1,-1) are orthogonal.
- ZW-ORTHOGONAL-VECTORS-004 The zero vector of ℝ^n is orthogonal to:
- ZW-ORTHOGONAL-VECTORS-005 Which of these vectors is orthogonal to (1,-2,2)?
- ZW-ORTHOGONAL-VECTORS-007 For any (a,b)≠(0,0), a vector orthogonal to (a,b) in ℝ^2 is:
- ZW-ORTHOGONAL-VECTORS-008 Let u,v be nonzero with u· v=0. Then:
- ZW-ORTHOGONAL-VECTORS-009 Which vector is orthogonal to both (1,0,1) and (0,1,1)?