Exercise · ZW-DOT-PRODUCT-010 · ★★★ Advanced
If \(u\cdot u=9\) and \(v\cdot v=4\), what is \((u+v)\cdot(u-v)\)?
Choose one option.
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- C. 5
Explanation
Expanding: \(u\cdot u-u\cdot v+v\cdot u-v\cdot v=9-4=5\); the cross terms cancel by commutativity.
Review the concept: Dot product
The dot product of two vectors in \(\mathbb{R}^n\) is the number obtained by multiplying their coordinates one by one and adding the results.
\[u\cdot v=u_1v_1+u_2v_2+\dots+u_nv_n\]
More practice problems: dot product
- ZW-DOT-PRODUCT-001 Compute (1,2,3)·(4,-5,6).
- ZW-DOT-PRODUCT-002 Compute (2,-1,0,3)·(1,4,5,-2).
- ZW-DOT-PRODUCT-003 The dot product of two vectors in ℝ^n is:
- ZW-DOT-PRODUCT-004 Compute (7,-2,5)·(1,0,0).
- ZW-DOT-PRODUCT-005 Compute (3,-4,12)·(3,-4,12).
- ZW-DOT-PRODUCT-006 For which k does (k,2,-1)·(3,k,4)=0 hold?
- ZW-DOT-PRODUCT-007 If u· v=5 and u· w=-2, what is u·(2v-3w)?
- ZW-DOT-PRODUCT-008 Which of these statements is false?