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The distance of point p(3,4,5) from the ...

The distance of point p(3,4,5) from the YZ- plane is

A

3 units

B

4 units

C

5 units

D

15 units

Text Solution

AI Generated Solution

The correct Answer is:
To find the distance of the point P(3, 4, 5) from the YZ-plane, we can follow these steps: ### Step 1: Understand the YZ-plane The YZ-plane is defined as the plane where the x-coordinate is zero. Therefore, any point on the YZ-plane has the form (0, y, z). ### Step 2: Identify the coordinates of point P The coordinates of point P are given as (3, 4, 5). Here, the x-coordinate is 3, the y-coordinate is 4, and the z-coordinate is 5. ### Step 3: Use the formula for distance from the YZ-plane The distance \( d \) of a point from the YZ-plane is equal to the absolute value of its x-coordinate. This can be expressed mathematically as: \[ d = |x| \] ### Step 4: Substitute the x-coordinate For point P(3, 4, 5), the x-coordinate is 3. Therefore, we substitute this value into the formula: \[ d = |3| \] ### Step 5: Calculate the distance Since the absolute value of 3 is simply 3, we have: \[ d = 3 \] ### Conclusion Thus, the distance of point P(3, 4, 5) from the YZ-plane is 3 units.
To find the distance of the point P(3, 4, 5) from the YZ-plane, we can follow these steps: ### Step 1: Understand the YZ-plane The YZ-plane is defined as the plane where the x-coordinate is zero. Therefore, any point on the YZ-plane has the form (0, y, z). ### Step 2: Identify the coordinates of point P The coordinates of point P are given as (3, 4, 5). Here, the x-coordinate is 3, the y-coordinate is 4, and the z-coordinate is 5. ...
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Knowledge Check

  • The distance of the point P(-3,4,5) from yz plant is

    A
    3 units
    B
    4 units
    C
    5 units
    D
    none of these

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