Question

Vector A

v has x and y components of 4 units and 2 units, respectively and vector

B

v has the corresponding components of -9 units and 3 units respectively. Find

(a) the vector components of their resultant,

(b) the magnitude and direction of their resultant.
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Answer 1

To find the vector components of the resultant of vectors A and B, we can simply add their corresponding components. The magnitude of the resultant vector is 5*sqrt(2) units and its direction is -45 degrees.

Step-by-step explanation:

To find the vector components of the resultant of vectors A and B, we can simply add their corresponding components. The x-component of the resultant vector is the sum of the x-components of A and B, and the y-component is the sum of the y-components of A and B.

So, the x-component of the resultant is 4 + (-9) = -5 units, and the y-component of the resultant is 2 + 3

= 5 units.

Therefore, the vector components of the resultant are (-5, 5) units.

To find the magnitude of the resultant vector, we can use the Pythagorean theorem.

The magnitude is given by the square root of the sum of the squares of the components.

Using the formula, the magnitude of the resultant vector is sqrt((-5)^2 + 5^2) = sqrt(25 + 25) = sqrt(50)

= 5*sqrt(2) units.

The direction of the resultant vector can be found using the tangent function. The direction angle is given by the arctan of the y-component divided by the x-component.

So, the direction angle of the resultant vector is arctan(5/(-5)) = arctan(-1)

= -45 degrees.