Let a vector α i ^ + β j ^ be obtained by rotating the vector 3 i ^ + j ^ by an angle 45 ° about the origin in counterclockwise direction in the first quadrant. Then the area (in sq. units) of triangl

Question

Let a vector α i ^ + β j ^ be obtained by rotating the vector 3 i ^ + j ^ by an angle 45 ° about the origin in counterclockwise direction in the first quadrant. Then the area (in sq. units) of triangle having vertices α , β , 0 , β and 0 , 0 is equal to

TestHub · Accepted Answer

Area of Δ OA ' B = 1 2 OA ' cos 15 ° × OA ' sin 15 ° = 1 2 OA ' 2 sin 30 ° 2 Now, O A = O A ' , since rotation will not change the magnitude. = 3 + 1 × 1 8 = 1 2 sq. units

Mathematics - Vector Question with Solution | TestHub

Options:

Doubts & Discussion