Question

A vector in x-y plane has a magnitude 30 unts & makes con angle 37° with se-axis. The vector can be written a a as-​

Answer 1

Answer:

∴ option (4), (24i + 18j) is correct.

Explanation:

The unit vector along the x-axis is i and its magnitude is 1

1. The given vector is (24i + 24j)

Magnitude of the vector

= √(24² + 24²) ≠ 30

2. The given vector is (18i + 24j)

Magnitude of the vector

= √(18² + 24²) = 30

If θ be the angle between i and (18i + 24j), then

θ = cos⁻¹ [ { (18i + 24j) . i } / 30 * 1 ]

= cos⁻¹ (18/30) ≈ 53.13°

3. The given vector is (18i + 18j)

Magnitude of the vector

= √(18² + 18²) ≠ 30  

4. The given vector is (24i + 18j)

Magnitude of the vector  

= √(24² + 18²) = 30

If θ be the angle between i and (18i + 24j), then

θ = cos⁻¹ [ { (24i + 18j) . i } / 30 * 1 ]

= cos⁻¹ (24/30) = 37°

∴ option (4), (24i + 18j) is correct.