Answer: The magnitude of B+Q is √69 and the magnitude of B-Q is √41.
Step-by-step explanation:
Let's calculate the magnitude of B+Q and B-Q.
First, we'll start with B+Q. We know that B is equal to 3i + 4j and Q is equal to 5i - 2j + 1k. So, to find B+Q, we simply add the corresponding components of B and Q:
(3i + 4j) + (5i - 2j + 1k) = 8i + 2j + 1k
To find the magnitude of B+Q, we use the Pythagorean theorem, just like we would in finding the distance between two points in a plane. But since we have three dimensions (i, j, and k), we have to square the values of 8i, 2j, and 1k and add them up, and then take the square root of the result.
The magnitude of B+Q is √(8^2+2^2+1^2) = √(64+4+1) = √69
Now, let's move on to B-Q. We know that B is equal to 3i + 4j and Q is equal to 5i - 2j + 1k. So, to find B-Q, we subtract the corresponding components of Q from B:
(3i + 4j) - (5i - 2j + 1k) = -2i + 6j - 1k
To find the magnitude of B-Q, we again use the Pythagorean theorem, just like we would in finding the distance between two points in a plane. But since we have three dimensions (i, j, and k), we have to square the values of -2i, 6j, and -1k and add them up, and then take the square root of the result.
The magnitude of B-Q is √((-2)^2+6^2+(-1)^2) = √(4+36+1) = √41
And there you have it! The magnitude of B+Q is √69 and the magnitude of B-Q is √41.