Calculating 2A + 3(B+C): Vector Addition

In summary, to find 2A + 3(B+C), we first find the individual vectors 2A and (B+C) by multiplying each component by the scalar and then adding them together. This results in the vector (16,10,11). This method is correct as a scalar can be multiplied to a vector to scale its magnitude without changing its direction.
  • #1
klm
165
0
vector A= (2,-1,1)
vec. B = ( 3, 0, 5)
vec. C = (1,4,-2)
what is 2A + 3(B+C)

this is what i did:
2A = 2(2,-1,1) = (4,-2, 2)

(B+C) = (4,4,3) x 3 = (12,12, 9)

2A + 3(B+C) = (16,10,11)

is this the correct way to think and do this problem?
 
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  • #2
Yes, you just add up the components because all vectors are the sum of their components; and of course, a scalar times a vector is just a vector of scaled up magnitude in the direction of the original vector.
 
  • #3
okay thank you! and is it all right to multiply like that? or is there some other rule for multiplying vectors?
 
  • #4
It is all right, because that is just a case of a scalar multiplying a vector.
 
  • #5
ok! thank you very much!
 

FAQ: Calculating 2A + 3(B+C): Vector Addition

What is vector addition?

Vector addition is the process of combining two or more vectors to create a new vector. It involves adding the corresponding components of each vector to determine the resulting magnitude and direction of the new vector.

What does 2A + 3(B+C) mean?

This notation represents the sum of two vectors A and B, and three times the sum of vectors B and C. In other words, it is the result of adding two vectors A and B, and then adding three times the combined vector of B and C.

How do you calculate 2A + 3(B+C)?

To calculate 2A + 3(B+C), you first need to determine the individual components of each vector. Then, add the corresponding components of A and B to determine the resulting vector AB. Next, add the components of B and C to determine the vector BC. Finally, multiply the vector BC by 3 and add it to vector AB to obtain the final result of 2A + 3(B+C).

Can you use vector addition for more than two vectors?

Yes, vector addition can be used for any number of vectors. The process involves adding the corresponding components of each vector to determine the final result. However, the order in which the vectors are added can affect the result, so it is important to follow a consistent order when adding multiple vectors.

What are some real-life applications of vector addition?

Vector addition has many real-life applications, such as determining the resulting force on an object that is acted upon by multiple forces, calculating the velocity and acceleration of an object moving in multiple directions, and predicting the direction and magnitude of wind and ocean currents. It is also used in various fields of science, engineering, and mathematics, such as physics, astronomy, and computer graphics.

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