The addition of vectors involve both magnitude and direction. In this case, we make use of a triangle to visualize the problem. The length of two sides were given while the measure of the angle between the two sides can be derived. We then assign variables for each of the given quantities.
Let:
b = length of one side = 8 m
c = length of one side = 6 m
A = angle between b and c = 90°-25° = 75°
We then use the cosine law to find the length of the unknown side. The cosine law results to the formula: a^2 = b^2 + c^2 -2*b*c*cos(A). Substituting the values, we then have: a = sqrt[(8)^2 + (6)^2 -2(8)(6)cos(75°)]. Finally, we have a = 8.6691 m.
Next, we make use of the sine law to get the angle, B, which is opposite to the side B. The sine law results to the formula: sin(A)/a = sin(B)/b and consequently, sin(75)/8.6691 = sin(B)/8. We then get B = 63.0464°. However, the direction of the resultant vector is given by the angle Θ which is Θ = 90° - 63.0464° = 26.9536°.
In summary, the resultant vector has a magnitude of 8.6691 m and it makes an angle equal to 26.9536° with the x-axis.
Answer:
We feel cold when tap or well water in winter because heat flows from hot body to cold body.
Explanation:
Our <em>body</em><em> </em><em>is</em><em> </em><em>in</em><em> </em><em>optimal</em><em> </em><em>status</em><em> </em><em>is</em><em> </em><em>a</em><em> </em><em>hot</em><em> </em><em>body</em><em> </em><em>and</em><em> </em><em>tap</em><em> </em><em>or</em><em> </em><em>we</em><em>ll</em><em> </em><em>water</em><em> </em><em>is</em><em> </em><em>a</em><em> </em><em>cold</em><em> </em><em>body</em><em>.</em><em> </em><em>Theref</em><em>ore</em><em> </em><em>we</em><em> </em><em>feel</em><em> </em><em>cold</em><em>.</em>
Answer:
c = e > b = d > a
Explanation:
Given vectors are all unit vectors, therefore they have a magnitude of 1
<h3>Let a, b be two vectors and magnitude of cross product of these two vectors is (magnitude of a) × (magnitude of b) × (sine of angle between these two vectors)</h3>
As all are unit vectors their magnitude is 1 and therefore in this case the cross product between any two vectors depends on the sine of angle between those two vectors
In option a as both the vectors are same, the angle between them will be zero and sin0° will also be 0
In option b angle between those two vectors is 135° and sin135° is 1 ÷ √2
In option c angle between those two vectors is 90° and sin90° is 1
In option d angle between those two vectors is 45° and sin45° is 1 ÷ √2
In option e angle between those two vectors is 90° and sin90° is 1
So by comparison of magnitudes of cross products in each option, the order will be c = e > b = d > a
