The vector sum of two vectors of magnitude 10 units and 15 units can never be
A) 28 units
B) 22 units
C) 18 units
D) 8 units
28
28 it's y because P+Q》R》P-R
that is 10 +15》R》15-10
25》R》5
hence the possibility by the options given will be 28
here 》 denotes the greaterthanandequal to
A+B>Magnitude of resultant >A-B
10+15>R>|10-15|
=25>R>5
even if they are end to end, the sum will be 25.
28
Very nice
To find the vector sum of two vectors, we need to use vector addition. The magnitude of the vector sum is generally given by the formula:
|A + B| = √(A^2 + B^2 + 2ABcosθ)
Where A and B are the magnitudes of the vectors, and θ is the angle between them.
In this case, we are given two vectors with magnitudes of 10 units and 15 units. Let's consider each option:
A) 28 units: To determine if this is possible, we need to determine the angle θ between the two vectors. We can use the cosine formula to solve for θ:
cosθ = (A^2 + B^2 - |A + B|^2) / (2AB)
Using the values A = 10, B = 15, and |A + B| = 28, we can plug them into the formula and calculate the cosine value. If the cosine value is between -1 and 1, it means there is an angle that satisfies the equation. However, if the cosine value is greater than 1 or less than -1, it means there is no angle that satisfies the equation.
B) 22 units: Similarly, we need to calculate the cosine value using the given magnitudes.
C) 18 units: Again, we need to calculate the cosine value.
D) 8 units: Once again, calculate the cosine value using the given magnitudes.
By calculating the cosine value for each option, we can determine if there exists an angle θ that satisfies the equation.