Question

Vector vector a has a magnitude of 29 units and points in the positive y-direction. when vector vector b is added to vector a , the resultant vector vector a + vector b points in the negative y-direction with a magnitude of 18 units. find the magnitude of vector b ?

Answer 1

Good morning.

We have:

$\mathsf{\overset{\to}{a} = 29\overset{\to}{j}}$

Where j is the unitary vector in the direction of the y-axis.

We have that 

$\mathsf{\overset{\to}{a}+\overset{\to}{b} = -18\overset{\to}{j}}$

We add the vector -a to both sides:

$\mathsf{\overset{\to}{b} = -18\overset{\to}{j} -\overset{\to}{a} = -18\overset{\to}{j} -29\overset{\to}{j}}\\ \\ \mathsf{\overset{\to}{b}=-47\overset{\to}{j}}$


Therefore, the magnitude of b is 47 units.

Answer 2

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 $\widehat{j}$

Unit vector in the negative y-direction are $- \widehat{j}$

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Vector $\overrightarrow{a}$ has a magnitude of 29 units and points in the positive y-direction :

$\boxed{ \overrightarrow{a} = 29 \widehat{j} }$ → Equation 1

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The resultant vector $\overrightarrow{a}$ + vector $\overrightarrow{b}$ points in the negative y-direction with a magnitude of 18 units :

$\overrightarrow{a} + \overrightarrow{b} = -18 \widehat{j}$

$29 \widehat{j} + \overrightarrow{b} = -18 \widehat{j}$ ← Equation 1

$\overrightarrow{b} = -18 \widehat{j} - 29 \widehat{j}$

$\boxed {\overrightarrow{b} = -47 \widehat{j}}$

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Conclusion :

Magnitude of vector $|\overrightarrow{b}|$ is 47 units

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The vector diagram of this problem can be drawn as seen in the attachment.

Blue arrow represents vector $\overrightarrow{a}$

Green arrow represents vector $\overrightarrow{b}$

Black arrow represents vector $\overrightarrow{a}$ + vector $\overrightarrow{b}$

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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