Draw the vector c⃗ =1.5a⃗ −3b⃗ . the length and orientation of the vector will be graded. the location of the vector is not important.

I made the drawing in the attached file.

I included two figures.

The upper figure shows the effect of:

- multiplying vector A times 1.5.
 It is drawn in red with dotted line.

- multiplying vector B times - 3 .
It is drawn in purple with dotted line.

In the lower figure you have the resultant vector: C = 1.5A - 3B.

The method is that you translate the tail of the vector -3B unitl the point of the vector 1,5A, preserving the angles.

Then you draw the arrow that joins the tail of 1,5A with the point of -3B after translation.

The resultant arrow is the vector C and it is drawn in black dotted line.
 

Further explanation

Vector is a quantity that has a value and direction

Vector can be symbolized in the form of directed line segments

while the length of the vector is denoted by | a |

Vectors can be written in the form of sequential pairs which show their coordinates in the Cartesian plane :  a (a₁, a₂)

with length

If the direction of vector a is reversed, we get the vector -a which has the same length but in the opposite direction

Operations on vectors include addition and subtraction. Addition of vectors a and vector b can be done in a triangular way where the base point of vector b coincides with the endpoint of vector a

The sum of the two is obtained by pulling the line segment from the base point of vector a to the endpoint of vector b which results in a new vector c

So a + b = c

If vector a is added by inverse b (-b) then the sum becomes a + (- b) = a-b

If a vector is multiplied by a scalar number (eg denoted by k) then the new vector becomes k | a |.

If k> 0, the new vector is in the direction of vector a, but if k <0 it will be in the opposite direction

There is an incomplete picture in the problem (picture attached), then a total of the vector is sought to obtain C = 1.5A-3B

If we multiply vector A by 1.5 then the length becomes 1.5 times vector A and in the same direction, so does vector B multiplied by the value of -3, which is 3 times the length of vector B but the direction is opposite, so we get vector C (attached picture) obtained by drawing a line from the starting point A and the endpoint B

Learn more

velocity position

link

identify the components of a vector

link

mathematical statement matches the vector operation

link

Keywords: vector, addition, subtraction

  sequence  is a continuous and distinctive band of  stars  that appears on plots of stellar  color  versus  brightness. these color-magnitude plots are known as  hertzsprung–russell diagramsafter their co-developers,  ejnar hertzsprungand  henry norris russell. stars on this band are known as  main-sequence stars  or  dwarf stars. these are the most numerous true stars in the universe, and include the earth's  sun.after condensation and ignition of a star, it generates  thermal energy  in its dense core region through  nuclear fusion  of  hydrogen  into  helium. during this stage of the star's lifetime, it is located on the main sequence at a position determined primarily by its mass, but also based upon its chemical composition and age. the cores of main-sequence stars are in  hydrostatic equilibrium, where outward thermal pressure from the hot core is balanced by the inward pressure of  gravitational collapse  from the overlying layers. the strong dependence of the rate of energy generation on temperature and pressure to sustain this balance. energy generated at the core makes its way to the surface and is radiated away at the  photosphere. the energy is carried by either  radiation  or  convection, with the latter occurring in regions with steeper temperature gradients, higher opacity or both.the main sequence is sometimes divided into upper and lower parts, based on the dominant process that a star uses to generate energy. stars below about 1.5 times the  mass of the sun  (1.5  m☉) primarily fuse hydrogen atoms together in a series of stages to form helium, a sequence called the  proton–proton chain. above this mass, in the upper main sequence, the nuclear fusion process mainly uses atoms of  carbon,  nitrogen  and  oxygen  as intermediaries in the  cno cycle  that produces helium from hydrogen atoms. main-sequence stars with more than two solar masses undergo convection in their core regions, which acts to stir up the newly created helium and maintain the proportion of fuel needed for fusion to occur. below this mass, stars have cores that are entirely radiative with convective zones near the surface. with decreasing stellar mass, the proportion of the star forming a convective envelope steadily increases. main-sequence stars below 0.4  m☉undergo convection throughout their mass. when core convection does not occur, a helium-rich core develops surrounded by an outer layer of hydrogen.in general, the more massive a star is, the shorter its lifespan on the main sequence. after the hydrogen fuel at the core has been consumed, the star  evolves  away from the main sequence on the hr diagram, into a  supergiant,  red giant, or directly to a  white dwarf.