If vector p is 6m in x direction and Q 8m in y direction what is value vector P+Q
AAAaannndd the bot gets it wrong yet again!
Since the two vectors are orthogonal, the magnitude of p+q is √(6^2+8^2) = 10, in the direction θ, where tanθ = 8/6. That is, P+Q makes an angle of 53.1° with the positive x-axis.
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To find the magnitude of vector P+Q, we can use the Pythagorean theorem, which states that the magnitude of a vector obtained by adding two orthogonal vectors can be found by taking the square root of the sum of the squares of the magnitudes.
The magnitude of vector P is 6m and the magnitude of vector Q is 8m. Thus, the magnitude of vector P+Q is √(6^2 + 8^2) = √(36 + 64) = √100 = 10m.
To find the direction of vector P+Q, we can use the tangent function. Tanθ = 8/6 = 4/3, where θ is the angle between vector P and the positive x-axis.
Using inverse tangent (tan^-1) or arctan, we find that θ is approximately 53.1°.
Therefore, vector P+Q has a magnitude of 10m in the direction of 53.1° with the positive x-axis.
To find the value of vector P + Q, we need to add the two vectors component-wise.
Given:
Vector P = 6m in the x-direction
Vector Q = 8m in the y-direction
To add vectors component-wise, we simply add the corresponding components together.
Adding the x-components:
P_x = 6m
Q_x = 0m (since Q is in the y-direction and has no x-component)
Adding the y-components:
P_y = 0m (since P is in the x-direction and has no y-component)
Q_y = 8m
Now, we can add the corresponding components together:
P_x + Q_x = 6m + 0m = 6m
P_y + Q_y = 0m + 8m = 8m
Therefore, the value of vector P + Q is a vector with components (6m, 8m).
To find the value of vector P+Q, we need to add the magnitudes of the two vectors in their respective directions.
Vector P is 6m in the x direction, so its x-component is 6m and its y-component is 0m.
Vector Q is 8m in the y direction, so its x-component is 0m and its y-component is 8m.
To find the x-component of the sum vector, we add the x-components of P and Q: 6m + 0m = 6m.
To find the y-component of the sum vector, we add the y-components of P and Q: 0m + 8m = 8m.
Therefore, the sum vector P+Q has a magnitude of 6m in the x direction and 8m in the y direction.