Add the vectors a = 4.0i + 3.0j and b = −13.0i + 7.0j.

Step 1: Write down the given vectors. The two vectors are: a = 4.0i + 3.0j; b = −13.0i + 7.0j Step 2: Add the corresponding components of the vectors. To find the sum of two vectors, add their i components together and their j components together. Let the sum be S = a + b. S = (4.0i + 3.0j) + (−13.0i + 7.0j) Group the i components and j components: S = (4.0 − 13.0)i + (3.0 + 7.0)j Step 3: Perform the addition for each component. For the i component: 4.0 − 13.0 = −9.0 For the j component: 3.0 + 7.0 = 10.0 Step 4: Write the resultant sum vector. S = −9.0i + 10.0j The correct option is B) −9.0i + 10.0j.

Add the vectors a = 4.0i + 3.0j and b = −13.0i + 7.0j.

Step 1: Write down the given vectors. The two vectors are: a = 4.0i + 3.0j; b = −13.0i + 7.0j Step 2: Add the corresponding components of the vectors. To find the sum of two vectors, add their i components together and their j components together. Let the sum be S = a + b. S = (4.0i + 3.0j) + (−13.0i + 7.0j) Group the i components and j components: S = (4.0 − 13.0)i + (3.0 + 7.0)j Step 3: Perform the addition for each component. For the i component: 4.0 − 13.0 = −9.0 For the j component: 3.0 + 7.0 = 10.0 Step 4: Write the resultant sum vector. S = −9.0i + 10.0j The correct option is B) −9.0i + 10.0j.

Solved: Add the vectors a = 4.0i + 3.0j and b = −13.0i…

Write down the given vectors.
The two vectors are:
$a = 4.0i + 3.0j$ $b = -13.0i + 7.0j$
Add the corresponding components of the vectors.
To find the sum of two vectors, add their $i$ components together and their $j$ components together.
Let the sum be $S = a + b$ .
$S = (4.0i + 3.0j) + (-13.0i + 7.0j)$
Group the $i$ components and $j$ components:
$S = (4.0 - 13.0)i + (3.0 + 7.0)j$
Perform the addition for each component.
For the $i$ component:
$4.0 - 13.0 = -9.0$
For the $j$ component:
$3.0 + 7.0 = 10.0$
Write the resultant sum vector.
$S = -9.0i + 10.0j$
The correct option is B) -9.0i + 10.0j.

Add the vectors a = 4.0i + 3.0j and b = -13.0i + 7.0j.

Answer

Step-by-step solution

Write down the given vectors.

Add the corresponding components of the vectors.

Perform the addition for each component.

Write the resultant sum vector.

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