# Add vector

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.

### Correct answer:

**Showing 1 comment:**

**Mathematican**

What is the component form of a vector?

The component form of a vector is given as (x, y), where x describes how far right or left a vector is going, and y represents how far up or down a vector is going.

When two points are given: P (the start point of the vector) and Q (the end point of the vector), the x component of the vector is the difference of x coordinates between endpoint Q and start point P, and y is the difference between the y coordinates of end Q and start point P.

Calculating the vector's magnitude uses the Pythagorean theorem to find the length of the hypotenuse of the formed right-angled triangle. Magnitude is the square root of x

The component form of a vector is given as (x, y), where x describes how far right or left a vector is going, and y represents how far up or down a vector is going.

When two points are given: P (the start point of the vector) and Q (the end point of the vector), the x component of the vector is the difference of x coordinates between endpoint Q and start point P, and y is the difference between the y coordinates of end Q and start point P.

Calculating the vector's magnitude uses the Pythagorean theorem to find the length of the hypotenuse of the formed right-angled triangle. Magnitude is the square root of x

^{2}+y^{2}. The distance formula can be used to find it from two points, P and Q.Tips for related online calculators

Our vector sum calculator can add two vectors given by their magnitudes and by included angle.

See also our right triangle calculator.

See also our right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

**geometry**- analytic geometry
- vector
**arithmetic**- square root
- absolute value
**planimetrics**- Pythagorean theorem
- right triangle

#### Units of physical quantities:

#### Grade of the word problem:

## Related math problems and questions:

- Mass point

Two equal forces of 30 Newtons act on a mass point. Find the magnitude of the resultant force if these forces form an angle of 42°. - Points OPQ

Point P is on line segment OQ. Given OP = 6, OQ = 4x - 3, and PQ = 3x, find the numerical length of OQ. - Quadrilateral PQRS

PQRS is a quadrilateral with P(4,4), S(8,8), and R(12,8). If vector PQ=4*vector SR, find the coordinates of Q. Solve it - Slope form

Find the equation of a line given the point X(8, 1) and slope -2.8. Arrange your answer in the form y = ax + b, where a and b are the constants. - Perpendicular 28823

Points A(1,2), B(4,-2) and C(3,-2) are given. Find the parametric equations of the line that: a) It passes through point C and is parallel to the line AB, b) It passes through point C and is perpendicular to line AB. - Vectors

Find the magnitude of the angle between two vectors u = (3; -5) and v = (10; 6) - General line equations

In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the slope form gives the line: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) the lin - Triangle's centroid

In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t - Coordinates 59763

The vectors v = (2.7; -1.8), w = (-3; 2.5) are given. Find the coordinates of the vectors: a = v + w, b = v-w, c = w-v, d = 2 / 3v - Parametric form

Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. - 3d vector component

The vector u = (3.9, u3), and the length of the vector u is 12. What is, is u3? - Line

Write an equation of a line parallel to To 9x + 3y = 8 That Passes Through The Point (-1, -4). Write in the form ax+by=c. - The graph

Given that (-5,8) is on the graph of f(x), find the corresponding point for the function f(x)-2. - North + west

Find the magnitude of the resultant of the given vectors: vector 1:2 m/s, north vector 2:7 m/s, west - Three points

Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d - Place vector

Place the vector AB if A (3, -1), B (5,3) in point C (1,3) so that AB = CO. - Rhombus

PQRS is a rhombus. Given that PQ=3 cm & height of rhombus is given 2 cm. Calculate its area.