Question

What is the magnitude of the vector (10i-10k) m/s?

Answer 1

"vector, v = 10i + 10k m/sec, magnitude, |v| = sqrt[10^2 + 10^2] = 10√2 m/sec >"

Answer 2

The magnitude of the vector (10i - 10k) m/s, is  14.14 m/s.

• A vector is a quantity that has both magnitude (size) and direction. In this case, the vector (10i - 10k) m/s can be thought of as representing a motion in a three-dimensional space with three axes: x, y, and z. The 'i' and 'k' components of the vector indicate the direction along the x and z axes, respectively.
• The magnitude of the vector represents the size of the motion, or how fast it is moving.

• To calculate the magnitude of a vector, we use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
• In this case, we treat the x and z components of the vector as the two shorter sides, and the magnitude of the vector as the longest side.

So to find the magnitude of the vector (10i - 10k) m/s,

we calculate the square root of the sum of the squares of its x and z components:

√$(10^2 + (-10)^2)$

= √(100 + 100)

= √200

= 10√2 m/s

This calculation gives us the magnitude of the vector (10i - 10k) m/s, which is approximately 14.14 m/s.

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