Question

a vector in x-y plane has magnitude 30 units and makes an angle 37° with X axis. the vector can be written as
(1) 24i + 24 j
(2) 18i + 24 j
(3) 18i + 18 j
(4) 24i + 18 j​

Answer 1

Answer:

The answer is option (4)

Explanation:

The detailed explanation is shown in the following image

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Answer 2

Solution:

The unit vector along 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.