Q. 74.0( 2 Votes )

# Find the angle between the vectors with direction ratios proportional to 2,3,–6 and 3,–4,5.

Answer :

Let us assume the direction ratios of vectors be (r_{1},r_{2},r_{3}) and (r_{4},r_{5},r_{6}).

Then,

⇒ (r_{1},r_{2},r_{3}) = (2,3,–6)

⇒ (r_{4},r_{5},r_{6}) = (3,–4,5)

We know that the angle between the vectors with direction ratios proportional to (a_{1},b_{1},c_{1}) and (a_{2},b_{2},c_{2}) is given by:

⇒

Using the above formula we calculate the angle between the vectors.

Let be the angle between the two vectors given in the problem.

⇒

⇒

⇒

⇒

⇒

⇒

∴ The angle between two given vectors is .

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