To find the value of |𝑷𝑸|, we need to find the distance between points P and Q.
The position vector from P to Q is given by:
𝑃𝑄 = (6 - 2, 𝑘 − 1 - 3, 15 - 5)
= (4, 𝑘 - 4, 10)
Since the position vectors are parallel, the direction ratios of the vector 𝑃𝑄 will be proportional to the coordinates of 𝑃.
So, we can write:
4/2 = (𝑘 - 4)/3
Cross multiplying, we get:
2(𝑘 - 4) = 4(3)
2𝑘 - 8 = 12
2𝑘 = 20
𝑘 = 10
Now, we can substitute the value of 𝑘 back into the position vector 𝑃𝑄:
𝑃𝑄 = (4, 𝑘 - 4, 10)
= (4, 10 - 4, 10)
= (4, 6, 10)
The distance between points P and Q, |𝑷𝑸|, can be found using the distance formula:
|𝑷𝑸| = √((6 - 4)^2 + (10 - 6)^2 + (10 - 5)^2)
= √(2^2 + 4^2 + 5^2)
= √(4 + 16 + 25)
= √45
Therefore, the value of |𝑷𝑸| is √45.
Given that, the coordinates of two points P and Q are (2, 3, 5) 𝑎𝑛𝑑 (6, 𝑘 − 1, 15)
respectively and that their position vectors are parallel, Calculate the value of |𝑷𝑸|. (4marks)
1 answer