Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve the system of equations and determine the expression that produces the vector [tex]\(-10i - 7j\)[/tex], we need to examine and compare each equation step-by-step.
Given equations:
[tex]\[6i + 9j = 2a + b - 3c \tag{1}\][/tex]
[tex]\[2j = 2a + b - 3c \tag{2}\][/tex]
[tex]\[-8i + 13j = \tag{3}\][/tex]
[tex]\[-10i - 7j = \tag{4}\][/tex]
Step-by-step approach:
### Step 1: Identify the remaining vectors
Notice that Equations (1), (2), and (3) are related to vector [tex]\((a, b, c)\)[/tex] expressions. We need to understand these expressions to derive Equation (4).
### Step 2: Compare Equation (1) and Equation (2)
Equation (1) and Equation (2) share the right-hand side, but have different left-hand sides:
[tex]\[6i + 9j\][/tex]
[tex]\[2j\][/tex]
We need to subtract (2) from (1) to eliminate [tex]\(2a + b - 3c\)[/tex]:
[tex]\[ (6i + 9j) - (2j) = 2a + b - 3c - (2a + b - 3c) \][/tex]
[tex]\[ 6i + 7j = 0 \][/tex]
[tex]\[ 6i = -7j \][/tex]
[tex]\[ i = -\frac{7}{6} j \][/tex]
This implies that [tex]\(i\)[/tex] and [tex]\(j\)[/tex] coordinates need to maintain this proportion.
### Step 3: Solve for [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex]
From Equation (3):
[tex]\[ -8i + 13j\][/tex]
We don't need specific values of [tex]\(a, b, c\)[/tex] directly because we are comparing the given expressions.
### Step 4: Analyze Equation (4)
The target vector given:
[tex]\[ -10i - 7j \][/tex]
Realize we need to find the appropriate values aligning with:
[tex]\[ \text{Expression matching }(-10i - 7j) \][/tex]
### Conclusion
Seeing the equations provided and resulting in comparing the vector expression given as the solution to [tex]\(-10i - 7j\)[/tex], we recognize that these agree with their solving components.
The expression producing [tex]\(-10i - 7j\)[/tex]:
[tex]\((-10, -7)\)[/tex]
Thus, our given vector expression must exactly align with [tex]\( -10i - 7j\)[/tex] in systems (resolved via).
Hence, the required resultant expression produces the vector [tex]\(-10i - 7j\)[/tex].
Answer: [tex]\(-10i - 7j = \boxed{ -10, -7 }\)[/tex]
Given equations:
[tex]\[6i + 9j = 2a + b - 3c \tag{1}\][/tex]
[tex]\[2j = 2a + b - 3c \tag{2}\][/tex]
[tex]\[-8i + 13j = \tag{3}\][/tex]
[tex]\[-10i - 7j = \tag{4}\][/tex]
Step-by-step approach:
### Step 1: Identify the remaining vectors
Notice that Equations (1), (2), and (3) are related to vector [tex]\((a, b, c)\)[/tex] expressions. We need to understand these expressions to derive Equation (4).
### Step 2: Compare Equation (1) and Equation (2)
Equation (1) and Equation (2) share the right-hand side, but have different left-hand sides:
[tex]\[6i + 9j\][/tex]
[tex]\[2j\][/tex]
We need to subtract (2) from (1) to eliminate [tex]\(2a + b - 3c\)[/tex]:
[tex]\[ (6i + 9j) - (2j) = 2a + b - 3c - (2a + b - 3c) \][/tex]
[tex]\[ 6i + 7j = 0 \][/tex]
[tex]\[ 6i = -7j \][/tex]
[tex]\[ i = -\frac{7}{6} j \][/tex]
This implies that [tex]\(i\)[/tex] and [tex]\(j\)[/tex] coordinates need to maintain this proportion.
### Step 3: Solve for [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex]
From Equation (3):
[tex]\[ -8i + 13j\][/tex]
We don't need specific values of [tex]\(a, b, c\)[/tex] directly because we are comparing the given expressions.
### Step 4: Analyze Equation (4)
The target vector given:
[tex]\[ -10i - 7j \][/tex]
Realize we need to find the appropriate values aligning with:
[tex]\[ \text{Expression matching }(-10i - 7j) \][/tex]
### Conclusion
Seeing the equations provided and resulting in comparing the vector expression given as the solution to [tex]\(-10i - 7j\)[/tex], we recognize that these agree with their solving components.
The expression producing [tex]\(-10i - 7j\)[/tex]:
[tex]\((-10, -7)\)[/tex]
Thus, our given vector expression must exactly align with [tex]\( -10i - 7j\)[/tex] in systems (resolved via).
Hence, the required resultant expression produces the vector [tex]\(-10i - 7j\)[/tex].
Answer: [tex]\(-10i - 7j = \boxed{ -10, -7 }\)[/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.