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At what value of angle between two vectors will the resultant of the two vectors be maximum?

yan [13]

The resultant is maximum when the angle between the two vectors is zero

Explanation:

The formula to calculate the resultant of two vectors A, B is the following:

$R=\sqrt{A^2+B^2+2ABcos \theta}$

where

A is the magnitude of vector A

B is the magnitude of vector B

$\theta$ is the angle between the directions of A and B

This formula can be derived by applying the parallelogram law.

From the formula, we observe that:

- When $\theta=0^{\circ}$ (vectors A and B parallel), $cos \theta = 1$ . so the resultant becomes simply

$R=\sqrt{A^2+B^2 + 2AB}=\sqrt{(A+B)^2}=A+B$

- When $\theta = 90^{\circ}$ (vectors A and B perpendicular), $cos \theta = 0$ , so the resultant becomes

$R=\sqrt{A^2+B^2}$

- When $\theta=180^{\circ}$ (vectors A and B anti-parallel), $cos \theta = -1$ , so the resultant becomes

$R=\sqrt{A^2+B^2 - 2AB}=\sqrt{(A-B)^2}=|A-B|$

By looking at the three cases and at the formula, we see that the maximum value of the resultant is when the angle between the two vectors is zero, since in that case the resultant is simply obtained by adding the magnitudes of the two vectors.

Learn more about vector addition:

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3 0

3 years ago

I desperately need help with my Physics Exam I am failing this class will mark Brainliest to whoever helps the most: PART 1 (I d

GREYUIT [131]

Option 2nd is correct

last option is correct

6 0

2 years ago

What is the drawback to use period of pendulum as time standard

Vadim26 [7]

The time period of a simple pendulum depends upon its length and value of'g'at any place. The period of the pendulum of fixed length

3 0

3 years ago

A 100.0 mL sample of 1.020 M HCl is mixed with a 50.0 mL sample of 2.040 M NaOH in a Styrofoam cup. If both solutions were initi

I am Lyosha [343]

Answer:

$t_2 = 33.793$

Explanation:

Given data:

0.1 L HCl × 1.020 mol/L = 0.102 mol HCL

0.05 L NaOH × 2.040 mol/L = 0.102 mol NaOH

NaOH + HCl \rightarrow H_2O + NaCl

0.102 mol HCl /1 mol HCl × 1 mol H2O = 0.102 mol H2O

0.102 mol H2O / 1 mol H2O × 57000 J = 5814 J

$V(t ) = V_1+V_2 = 100 + 50 = 150 mL$

M(t)=150*1=150 g

we know that heat energy is given as

$Q = mc(t_2 - t_1)$

where c is specific heat

total energy released is = 57 \times 0.102 = 5.814 kJ

$5814 = 150 \times 4.184 \times (t_2 - 24.53)$

$t_2 = 33.793$

8 0

3 years ago

A force of 20 N is exerted by an electric field on a test charge of 8.0 x 10² C at a point, P. What is the electric field streng

kenny6666 [7]

Answer:

the answer is equal to 1.6N/C

5 0

2 years ago