Respuesta :

aachen

Answer:

|A| = 8.06

Explanation:

Given that

Vector A, [tex]A=4i+7j[/tex]

We need to find the magnitude of the vector. Let the vector is R = ai + bj. The magnitude of this vector is given by :

[tex]|R|=\sqrt{a^2+b^2}[/tex]

In this given question, a = 4 and b = 7

The magnitude of vector A is given by :

[tex]|A|=\sqrt{4^2+7^2}[/tex]

|A| = 8.06

So, the magnitude of given vector is 8.06. Hence, this is the required solution.

The magnitude of the vector is [tex]\boxed{\sqrt {65} \,{\text{units}}}[/tex] or [tex]\boxed{8.06\,{\text{units}}}[/tex].

Further Explanation:

Given:

The givenvector is [tex]\vec a = 4\hat i + 7\hat j[/tex].

Concept:

A vector is a quantity which has the magnitude of the quantity as well as the direction for the complete expression of the quantity whereas the units that require only the magnitude of the quantity for its expression, they are called as the scalar quantities.

The magnitude of the vector of any quantity denotes the amount of the particular quantity held by the vector.

The magnitude of a vector [tex]\vec A = x\hat i + y\hat j[/tex] is calculated as:

[tex]\boxed{\left| {\vec A} \right| = \sqrt {{x^2} + {y^2}} }[/tex]   …… (1)                                                          

Substitute [tex]4[/tex] for [tex]x[/tex] and [tex]7[/tex] for [tex]y[/tex] in equation (1).

[tex]\begin{aligned}\left| {\vec A} \right| &= \sqrt {{4^2} + {7^2}}\\&= \sqrt {65}\\&= 8.06\,{\text{units}}\\\end{aligned}[/tex]  

Therefore, the magnitude of the vector is [tex]\boxed{\sqrt {65} \,{\text{units}}}[/tex] or [tex]\boxed{8.06\,{\text{units}}}[/tex].

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Answer Details:

Grade: High School

Chapter: Vectors and Scalars

Subject: Physics

Keywords:  Vectors, magnitude, direction, scalar, require direction, r epresentation, physical quantity, amount of quantity, physical quantity, 4i+7j.