The resultant of two perpendicular vectors a and b is given by the Pythagorean theorem as √(a² + b²).

Given that the resultant makes an angle of 30 degrees with vector a, we can use the cosine of the angle to find the ratio of the magnitudes of vectors a and b.

Cosine of the angle θ between two vectors is given by the dot product of the vectors divided by the product of their magnitudes. In this case, cos(30) = a / √(a² + b²).

Solving for b/a gives us:

b/a = √(a² / cos²(30) - a²)

b/a = √(2a² - a²)

b/a = a√(1)

So, the ratio of their magnitudes is 1:1.

Question

The resultant of two perpendicular vectors a and b is given by the Pythagorean theorem as √(a² + b²).

Given that the resultant makes an angle of 30 degrees with vector a, we can use the cosine of the angle to find the ratio of the magnitudes of vectors a and b.

Cosine of the angle θ between two vectors is given by the dot product of the vectors divided by the product of their magnitudes. In this case, cos(30) = a / √(a² + b²).

Solving for b/a gives us:

b/a = √(a² / cos²(30) - a²)

b/a = √(2a² - a²)

b/a = a√(1)

So, the ratio of their magnitudes is 1:1.

Knowee AI · Accepted Answer

The resultant of two perpendicular vectors a and b is given by the Pythagorean theorem as √(a² + b²).

Given that the resultant makes an angle of 30 degrees with vector a, we can use the cosine of the angle to find the ratio of the magnitudes of vectors a and b.

Cosine of the angle θ between two vectors is given by the dot product of the vectors divided by the product of their magnitudes. In this case, cos(30) = a / √(a² + b²).

Solving for b/a gives us:

b/a = √(a² / cos²(30) - a²)

b/a = √(2a² - a²)

b/a = a√(1)

So, the ratio of their magnitudes is 1:1.

The resultant of two perpendicular vectors (a"⃗ and b"⃗ ) make an angle of 30o with vector a"⃗ . The ratio of theirmagnitudes -. is

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The resultant of two perpendicular vectors ( $\vec{a}$ and $\vec{b}$ ) make an angle of $30^{\circ}$ with vector $\vec{a}$ . The ratio of their magnitudes is...

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