OA = (1,3,-1) and OD = (-1,0, n) find the value of n for which the length of AD is 7 units

n = 5

Step-by-step explanation:

0A = (1,3,-1) and OD = (-1,0, n)

AD = √ (-1-1) ^2 + (0-3) ^2 + (n - (-1)) ^2

7 = √ (-2) ^2 + (-3) ^2 + (n+1) ^2

7 = √4 + 9 + (n+1) ^2

Now squaring both sides we have:

7^2 = (√4 + 9 + (n+1) ^2) ^2

49 = 4 + 9 + (n+1) ^2

49 = 13 + (n+1) ^2

49 - 13 = (n+1) ^2

36 = (n+1) ^2

Taking the square root of both sides we have:

√36 = √ (n+1) ^2

6 = (n+1)

6 = n + 1

6 - 1 = n

5 = n

Therefore n = 5