Q10 of 76 Page 477

Find the angle between the following pairs of lines:

We know that

If θ is the acute angle between and , then


……(i)


(i) and


Here and


So, from (i), we have


……(ii)


⇒


⇒


And


Now,


⇒


⇒ By (ii), we have


⇒


⇒


(ii) and


Here, and


So, from (i), we have


…(iii)


⇒


⇒


And


Now,


⇒


⇒ By (iii), we have


⇒


⇒


More from this chapter

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1

Find the vector and the cartesian equations of the lines that passes through the origin and (5, –2, 3).

 9

. Find the vector and the cartesian equations of the line that passes through the points (3, –2, –5), (3, –2, 6).

 11

. Find the angle between the following pair of lines:

 12

Find the values of p so that the lines are at right angles.