# Common Core: High School - Number and Quantity : Magnitude and Direction of a Vector Sum: CCSS.Math.Content.HSN-VM.B.4b

## Example Questions

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### Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

Here is a visual representation of what we just found.

### Example Question #2 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

### Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

### Example Question #2 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

### Example Question #3 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

### Example Question #4 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

### Example Question #5 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

### Example Question #56 : Vector & Matrix Quantities

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

### Example Question #6 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If , and , and the angle in between them is , find the magnitude of the resultant vector.

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is . Suppose that , and , then

### Example Question #58 : Vector & Matrix Quantities

If , and , and the angle in between them is , find the magnitude of the resultant vector.