# How do I find the angle between the planes 5(x+1) + 3(y+2) + 2z = 0 and x + 3(y-1) + 2(z+4) = 0?

be their normals.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the angle between two planes, we can use the formula:

cos(theta) = |a₁ * a₂ + b₁ * b₂ + c₁ * c₂| / sqrt(a₁² + b₁² + c₁²) * sqrt(a₂² + b₂² + c₂²)

Where (a₁, b₁, c₁) and (a₂, b₂, c₂) are the normal vectors of the planes.

For the first plane, the coefficients of x, y, and z are (5, 3, 2), and for the second plane, the coefficients are (1, 3, 2).

Using these coefficients, we can calculate the angle between the planes by substituting them into the formula:

cos(theta) = |5 * 1 + 3 * 3 + 2 * 2| / sqrt(5² + 3² + 2²) * sqrt(1² + 3² + 2²)

cos(theta) = |5 + 9 + 4| / sqrt(38) * sqrt(14)

cos(theta) = |18| / sqrt(38 * 14)

cos(theta) = 18 / sqrt(532)

cos(theta) ≈ 0.983

Now, to find the angle, we take the inverse cosine of 0.983:

theta ≈ arccos(0.983)

theta ≈ 10.08 degrees

So, the angle between the planes is approximately 10.08 degrees.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the unit vector having the same direction as vector u = i - 6 j + 5 k?
- How do you find a unit vector that is orthogonal to both u= - 6i + 4j + k and v= 3i + j + 5k?
- How do you find the scalar and vector projections of b onto a given #a = ‹3, 2, 1›#, #b = ‹0, 1, 3›#?
- How to find a vector A that has the same direction as ⟨−8,7,8⟩ but has length 3 ?
- What is meant by a component of a vector?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7