Exercise · ZW-DOT-PRODUCT-007 · ★★☆ Intermediate
If \(u\cdot v=5\) and \(u\cdot w=-2\), what is \(u\cdot(2v-3w)\)?
Choose one option.
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- D. 16
Explanation
By linearity: \(2(u\cdot v)-3(u\cdot w)=10+6=16\). Watch the sign of \(-3\cdot(-2)\).
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-008 Which of these statements is false?
- ZW-DOT-PRODUCT-009 If u· v=u· w and u≠ 0, what can be concluded?