Math Problem Statement
Find 2π, β3π, π + π, and 3π β 4π for the given vectors π and π.
π = β6, 7, π = 6, β9
2π
= β3π
= π + π
= 3π β 4π=
Solution
Given two vectors:
We are asked to find the following quantities:
Step 1: Calculate
Multiply vector by 2:
Step 2: Calculate
Multiply vector by -3:
Step 3: Calculate
Add vectors and :
Step 4: Calculate
Multiply vector by 3 and vector by 4, then subtract: Now subtract:
Final Results:
Do you have any questions or would you like more details?
5 Related Questions:
- How do you multiply a scalar with a vector?
- How is vector addition performed geometrically?
- What is the difference between scalar multiplication and vector subtraction?
- How do vectors behave under matrix transformations?
- Can vectors of different dimensions be added?
Tip:
When performing vector arithmetic, ensure that you are consistent with the dimensions of the vectors to avoid mistakes.
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Math Problem Analysis
Mathematical Concepts
Vector Arithmetic
Scalar Multiplication
Vector Addition
Vector Subtraction
Formulas
Scalar Multiplication: k * (a, b) = (k * a, k * b)
Vector Addition: (a, b) + (c, d) = (a + c, b + d)
Vector Subtraction: (a, b) - (c, d) = (a - c, b - d)
Theorems
Basic Properties of Vectors
Suitable Grade Level
Grades 9-12
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