Question

Find the sum of the vectors <−5,2> and <6,9>. Then find the magnitude and direction of the resultant vector. Round angles to the nearest degree and other values to the nearest tenth.

Answer 1

see below

Explanation:

To find the magnitude of the resultant vector, use the Distance Formula.

|<1,11>|=(1−0)2+(11−0)2−−−−−−−−−−−−−−−−√

Simplify

|<1,11>|=1+121−−−−−−√

Simplify.

|<1,11>|=122−−−√

Take the square root and round to the nearest tenth.

|<1,11>|≈11.0

The angle A

measure formed by the resultant vector and the x

-axis gives the direction of the resultant vector.

tanA=111=11

Solve for m∠A

m∠A=tan−1(11)

Round to the nearest degree.

m∠A≈85°

Therefore, the resultant vector is <1,11>

, the magnitude of the vector is approximately 11

, the direction of the vector is approximately 85°

hope this helps!

Answer 2

Sum = <1,11>

Magnitude = 11.05

Direction = 84.81

Explanation:

Given.

Let Vector A = <-5,2>

Vector B = <6,9>

Sum = A + B

Sum = <-5,2> + <6, 9>

Sum = <-5 + 6, 2 + 9>

Sum = <1,11>

where x = 1 and y = 11

Calculating the magnitude...

Magnitude = √(x² + y²)

Magnitude = √(1² + 11²)

Magnitude = √(1 + 121)

Magnitude = √122

Magnitude = 11.04536101718726

Magnitude = 11.05 --- Approximated

Calculating the vector direction

Direction of a vector is calculated by tan^-1 (y/x)

Direction = tan^-1(11/1)

= tan^-1(11)

= 84.80557109226519

= 84.81° ---- Approximated