A point on a line has coordinates (p + 1, p - 3, √2p) where p is any real number. What are the direction cosines of the line?

If l, m, n are the direction cosines of the line x - 1 = 2(y + 3) = 1 - z, then what is l ⁴+ m ⁴+ n ⁴equal to?

A straight line with direction cosines \(\left\langle {0,\;1,\;0} \right\rangle\) is

If a line has direction ratios < a + b, b + c, c + a >, then what is the sum of the squares of its direction cosines?

Consider the following statements :

1. The direction ratios of y-axis can be <0, 4, 0>

2. The direction ratios of a line perpendicular to z-axis can be <5, 6, 0>

Which of the statements given above is/are correct?

The direction ratios of the line perpendicular to the lines with direction ratios < 1, -2, -2 > and < 0, 2, 1 > are

What are the direction cosines of z-axis?

Consider the following statements:

1. A-line in space can have infinitely many direction ratios.

2. It is possible for certain lines that the sum of the squares of direction cosines can be equal to the sum of its direction cosines.

Which of the above statements is/are correct?

If α, β and γ are the angles which the vector \(\overrightarrow {OP} \)   (O being the origin) makes with the positive direction of the coordinate axes, then which of the following are correct?

1. cos ²α + cos ²β = sin ²γ

2. sin ²α + sin ²β = cos ²γ

3. sin ²α  + sin ²β + sin ²γ = 2

Select the correct answer using the code given below.

A point on a line has coordinates (p + 1, p - 3, √2p) where p is any real number. What are the direction cosines of the line?

If l, m, n are the direction cosines of the line x - 1 = 2(y + 3) = 1 - z, then what is l ⁴+ m ⁴+ n ⁴equal to?

Which of the following is the direction cosines of z, y and x-axis?

Determine the direction cosines of the unit vector perpendicular to the plane \(\vec{r} \cdot(2 \hat{\imath}-6 \hat{\jmath}-3 \hat{k})+1=0\) passing through the origin?