Vector A has a magnitude of 248 N and direction angles of α = 85°, β = 114°, and γ = 25°. Express Vector A in unit vector notation.

To find the direction cosines of the vector,

l = cos(α) = cos(85)
m = cos(β) = cos(114)
n = cos(γ) = cos(25)

Now, the unit vector can be represented as:

li + mj + nk (i, j, k, are orthogonal unit vectors)

=> Unit vector = cos(85)i + cos(114)j + cos(25)k

Vector = Magnitude * Unit Vector
= 248(cos(85)i + cos(114)j + cos(25)k)

To express vector A in unit vector notation, we first need to find the components of vector A in the x, y, and z directions.

Using the direction angles α, β, and γ, we can calculate the cosine of each angle. The cosine of an angle tells us the projection of the vector onto a specific axis.

The x-component of vector A, Ax, can be found using the equation:
Ax = magnitude of A * cos(β) * cos(γ)

The y-component of vector A, Ay, can be found using the equation:
Ay = magnitude of A * cos(α) * cos(γ)

The z-component of vector A, Az, can be found using the equation:
Az = magnitude of A * cos(α) * sin(β)

Now, let's substitute the given values into these equations and calculate Ax, Ay, and Az.

Ax = 248 N * cos(114°) * cos(25°)
Ay = 248 N * cos(85°) * cos(25°)
Az = 248 N * cos(85°) * sin(114°)

After calculating the values, we can express vector A in unit vector notation as:

Vector A = (Ax/|A|) i + (Ay/|A|) j + (Az/|A|) k

Where i, j, and k are the unit vectors in the x, y, and z directions respectively, and |A| is the magnitude of vector A.