Question

A vector makes angles 60° and 45° with x and y axes respectively. If the angle between the vector and x-y plane in degrees in 5n , find n​

Answer 1

Answer:

This is the answer of your question.

Answer 2

Concept:

• Vectors
• Resolution of vectors
• 3-dimensional vectors
• Direction cosines
• The direction cosines of a vector in analytical geometry are the cosines of the angles that the vector makes with the three positive coordinate axes.

Given:

• The angle between vector and x-axis α = 60°
• The angle between vector and y-axis β = 45°

Find:

• the value of n

Solution:

Z axis is perpendicular to the XY plane

γ = 90 - 5n

We know that

(cos α)^2 + (cos β)^2 + (cos γ)^2 = 1

(cos 60)^2 + (cos 45 )^2 + (cos γ)^2 = 1

1/4 + 1/2 +  (cos γ)^2 = 1

(cos γ)^2 = 1/4

cos γ = 1/2

γ = 60°

90° - 5n = 60°

5n = 30°

n = 6°

The value of n is 6°.

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