Question

A vector n of magnitude 8 units incline to x-axis at 45 degree and y-axis at 60 degree and an acute angle y z axis of a plane passing through a point root 2 - 11 and is not one to hundred equation in vector form

Answer 1

Given:

Magnitude = 8 units

x axis = 45 degree

y axis = 60 degree

Point = ( 2, -1, 1 )

To find:

The vector form.

Solution:

The angle of inclination on the x axis,

α = 45 degree

The angle of inclination on the y axis,

β = 60 degree

By formula,

cos^2 α + cos^2 β + cos^2 Υ = 1

Substituting,

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

1/2 + 1/4 + cos^2 Y = 1

Hence,

cos Y = 1/2

In vector form,

n^ = cos α i^ + cos β j^ + cos Y k^

Substituting,

We get,

1/√2 i^ + 1/2 j^ + 1/2 k^

Hence, in vector form 1/√2 i^ + 1/2 j^ + 1/2 k^