Question

ans plz..................3d geometry​

Answer 1

Answer:

Direction cosines are denoted as l,m,n where l, m, n refer to the cosine value of angles measured by the line on the x-axis, y-axis, z-axis respectively.

One important result to be remembers based on l, m, n is:

→ l² + m² + n² = 1

Coming to the question,

Angle made by the line with the positive x-axis is 2π/3

→ Cos ( 2π/3 ) = Cos ( π - π/3 ) = -1/2

Hence l = (-1/2)

Angle made by the line with the positive y-axis is π/3

→ Cos ( π/3 ) = 1/2

Hence m = 1/2

Now we are not given the angle made by line with the positive z-axis. Hence we use the result we know.

→ l² + m² + n² = 1

→ ( -1/2 )² + ( 1/2 )² + n² = 1

→ ( 1/4 ) + ( 1/4 ) + n² = 1

→ ( 1/2) + n² = 1

→ n² = 1 - ( 1/2 )

→ n² = 1/2

⇒ n = ± √( 1/2 )

⇒ n = ± ( 1/√2 )

Hence Option (A) is the right answer.

Answer 2

OPTION A IS THE ANSWER

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