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

true

step-by-step explanation: