# Working With Vectors Solutions

### Solution 1

``````u <- 4
v <- 8
u + v``````
``##  12``
``u - v``
``##  -4``
``u * v``
``##  32``
``u / v``
``##  0.5``
``u^v``
``##  65536``

Back to exercise

### Solution 2

``````u <- c(4, 5, 6)
v <- c(1, 2, 3)
u + v``````
``##  5 7 9``
``u - v``
``##  3 3 3``
``u * v``
``##   4 10 18``
``u / v``
``##  4.0 2.5 2.0``
``u^v``
``##    4  25 216``

Back to exercise

### Solution 3

``````u <- c(5, 6, 7, 8)
v <- c(2, 3, 4)
u + v``````
``````## Warning in u + v: longer object length is not a multiple of shorter object
## length``````
``##   7  9 11 10``
``u - v``
``````## Warning in u - v: longer object length is not a multiple of shorter object
## length``````
``##  3 3 3 6``
``u * v``
``````## Warning in u * v: longer object length is not a multiple of shorter object
## length``````
``##  10 18 28 16``
``u / v``
``````## Warning in u/v: longer object length is not a multiple of shorter object
## length``````
``##  2.50 2.00 1.75 4.00``
``u^v``
``````## Warning in u^v: longer object length is not a multiple of shorter object
## length``````
``##    25  216 2401   64``

R uses the recycle rule when vectors have different lengths, i.e. it re-uses elements from the shorter vector (starting at the beginning of the vector). In this case, it treats `v` as `c(2, 3, 4, 2)` (re-using its first element `2`).

Back to exercise

### Solution 4

#### Part a

``````u <- c(8, 9, 10)
v <- c(1, 2, 3)
w <- 0.5 * v
w <- u + w
w <- w^2
w``````
``##   72.25 100.00 132.25``

Now check with the original approach:

``````w <- (u + 0.5 * v) ^ 2
w``````
``##   72.25 100.00 132.25``

#### Part b

``````w1 <- u + 2
w2 <- u - 5
w <- w1 * w2
w <- w + v
w``````
``##  31 46 63``

Now check with the original approach:

``````w <- (u + 2) * (u - 5) + v
w``````
``##  31 46 63``

#### Part c

``````w1 <- u + 2
w2 <- u - 5
w2 <- w2 * v
w <- w1 / w2
w``````
``##  3.333333 1.375000 0.800000``

Now check with the original approach:

``````w <- (u + 2) / ((u - 5) * v)
w``````
``##  3.333333 1.375000 0.800000``

Back to exercise

### Solution 5

#### Part a

``````w <- ((u + v) / 2) + u
w``````
``##  12.5 14.5 16.5``

Now check with the original approach:

``````w <- u + v
w <- w / 2
w <- w + u
w``````
``##  12.5 14.5 16.5``

#### Part b

``````w <- (u^3) / (u-v)
w``````
``##   73.14286 104.14286 142.85714``

Now check with the original approach:

``````w1 <- u^3
w2 <- u - v
w <- w1 / w2
w``````
``##   73.14286 104.14286 142.85714``

Back to exercise

### Solution 6

The solution for this exercise is available in our eBook Start Here To Learn R – vol. 1: Vectors, arithmetic, and regular sequences.

Back to exercise

### Solution 7

The solution for this exercise is available in our eBook Start Here To Learn R – vol. 1: Vectors, arithmetic, and regular sequences.

Back to exercise

### Solution 8

The solution for this exercise is available in our eBook Start Here To Learn R – vol. 1: Vectors, arithmetic, and regular sequences.

Back to exercise

### Solution 9

The solution for this exercise is available in our eBook Start Here To Learn R – vol. 1: Vectors, arithmetic, and regular sequences.

Back to exercise