Answer :
Good morning.
We have:
[tex]\mathsf{\overset{\to}{a} = 29\overset{\to}{j}}[/tex]
Where j is the unitary vector in the direction of the y-axis.
We have that
[tex]\mathsf{\overset{\to}{a}+\overset{\to}{b} = -18\overset{\to}{j}}[/tex]
We add the vector -a to both sides:
[tex]\mathsf{\overset{\to}{b} = -18\overset{\to}{j} -\overset{\to}{a} = -18\overset{\to}{j} -29\overset{\to}{j}}\\ \\ \mathsf{\overset{\to}{b}=-47\overset{\to}{j}}[/tex]
Therefore, the magnitude of b is 47 units.
We have:
[tex]\mathsf{\overset{\to}{a} = 29\overset{\to}{j}}[/tex]
Where j is the unitary vector in the direction of the y-axis.
We have that
[tex]\mathsf{\overset{\to}{a}+\overset{\to}{b} = -18\overset{\to}{j}}[/tex]
We add the vector -a to both sides:
[tex]\mathsf{\overset{\to}{b} = -18\overset{\to}{j} -\overset{\to}{a} = -18\overset{\to}{j} -29\overset{\to}{j}}\\ \\ \mathsf{\overset{\to}{b}=-47\overset{\to}{j}}[/tex]
Therefore, the magnitude of b is 47 units.
The magnitude of vector b is 47 units
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Further explanation
Vector is quantity that has magnitude and direction.
One example of a vector is displacement.
Let us now tackle the problem !
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This problem is about Vector Diagram.
Assume :
Unit vector in the positive y-direction are [tex]\widehat{j}[/tex]
Unit vector in the negative y-direction are [tex]- \widehat{j}[/tex]
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Vector [tex]\overrightarrow{a}[/tex] has a magnitude of 29 units and points in the positive y-direction :
[tex]\boxed{ \overrightarrow{a} = 29 \widehat{j} }[/tex] → Equation 1
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The resultant vector [tex]\overrightarrow{a}[/tex] + vector [tex]\overrightarrow{b}[/tex] points in the negative y-direction with a magnitude of 18 units :
[tex]\overrightarrow{a} + \overrightarrow{b} = -18 \widehat{j}[/tex]
[tex]29 \widehat{j} + \overrightarrow{b} = -18 \widehat{j}[/tex] ← Equation 1
[tex]\overrightarrow{b} = -18 \widehat{j} - 29 \widehat{j}[/tex]
[tex]\boxed {\overrightarrow{b} = -47 \widehat{j}}[/tex]
[tex]\texttt{ }[/tex]
Conclusion :
Magnitude of vector [tex]|\overrightarrow{b}|[/tex] is 47 units
[tex]\texttt{ }[/tex]
The vector diagram of this problem can be drawn as seen in the attachment.
Blue arrow represents vector [tex]\overrightarrow{a}[/tex]
Green arrow represents vector [tex]\overrightarrow{b}[/tex]
Black arrow represents vector [tex]\overrightarrow{a}[/tex] + vector [tex]\overrightarrow{b}[/tex]
[tex]\texttt{ }[/tex]
Learn more
- Direction of Displacement : https://brainly.ph/question/1746541
- Scalar and Vector : https://brainly.ph/question/274572
- Weight : https://brainly.ph/question/545327
- Orientation of Vectors : https://brainly.ph/question/2121753
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Answer details
Grade: High School
Subject: Physics
Chapter: Vectors
