Question

what is the rectangular components of vector of a vector A, 15 Unit long when it form an angle with +x-axis of 50 degree ​

Answer 1

Answer:

It depends on how many dimensions are considered.

The angle between two vectors can be determined from their dot product:

cos(theta) = (vector_1 dot vector_2) / (||vector_1||*||vector_2||)

theta = arccos((vector_1 dot vector_2) / (||vector_1||*||vector_2||))

A vector lying along the x-axis is 1 x-hat.

In two dimensions, a vector parallel to one with equal rectangular components is 1 x-hat + 1 y-hat.

theta = arccos(((1 x-hat) dot (1 x-hat + 1 y-hat)) / (||1 x-hat||*||1 x-hat + 1 y-hat||))

theta = arccos(1 / (1 * SQRT(2))

theta = pi / 4 radians = 45 degrees

In three dimensions, the result is

theta = arccos(1 / SQRT(3)), which is approximately 0.955 radians or 54.7 degrees.

In n dimensions, the result is

theta = arccos(1 / SQRT(n))

Hope this helps and does not mislead or confuse you.

Explanation:

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