Vector Word Problems and Answers :

Here we are going to see how to solve vector word problems and answers.

Vector Word Problems and Answers - Practice Questions

Question 1 :

If G is the centroid of a triangle ABC, prove that GA vector + GB vector  + GC vector = 0.

Solution :

From the given information, let us draw a rough diagram. Centroid of the triangle divides in the ratio 2 : 1.

OA vector  =  a vector

OB vector =  b vector

OC vector  =  c vector

OG vector  =   [m (OD vector) + n (OA vector)] / (m + n)

OG vector  =   [2(OD vector) + 1(OA vector)] / (2+1)

OG vector  =   [2(OD vector) + 1(OA vector)] / 3  ---(1)

D is the midpoint of the side BC.

OD vector  =  (OB vector + OC vector) /2

By applying the value of OD in (1), we get

OG vector  =   (OB vector + OC vector + OA vector)/3

3OG vector  =  OA vector + OB vector + OC vector

(OA-OG) vector + (OB-OG) Vector + (OC-OG) vector  =  0

GA vector + GB vector + GC vector  =  0

Question 2 :

Let A, B, and C be the vertices of a triangle. Let D,E, and F be the midpoints of the sides BC, CA, and AB respectively. Show that AD vector + BE vector + CF vector  = 0.

Solution :

Let us draw a picture using the given information. OA vector  =  a vector

OB vector  =  b vector

OC vector  =  c vector

OD = (OB + OC)/2  =  (b + c) / 2

OE = (OA + OC)/2  =  (a + c) / 2

OF = (OA + OB)/2  =  (a + b) / 2

AD vector  =  (OD - OA) vector  ----(1)

By applying OD in (1), we get

=  ((b + c)/2) - a

=  (b + c - 2a)/2

BE vector :

BE vector  =  (OE - OB) vector  ----(2)

By applying OE in (2), we get

=  ((a + c)/2) - b

=  (a + c - 2b)/2

CF vector :

CF vector  =  (OF - OC) vector  ----(3)

By applying OF in (3), we get

=  ((a + b)/2) - c

=  (a + b - 2c)/2

AD vector + BE vector + CF vector  = 0

=  [(b + c - 2a) + (a + c - 2b) +  (a + b - 2c)]/2

=  0

Hence it is proved

Question 3 :

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then prove that AB vector + AD vector + CB vector + CD vector = 4EF vector.

Solution : Since F is the midpoint of the side BD,

AF vector  =  (AB vector + AD vector) /2

2AF vector  =  AB vector + AD vector  ----(1)

CF vector  =  (CB vector + CD vector) /2

2CF vector  =  CB vector + CD vector  ----(2)

(1) + (2)

2AF vector + 2CF vector

=  (AB vector + AD vector) + (CB vector + CD vector)

2(AF vector + CF vector)

=  (AB vector + AD vector) + (CB vector + CD vector)

Instead of AF + CF, we may write 2EF (using midpoint formula vice versa)

AB vector + AD vector + CB vector + CD vector  =  4  EF After having gone through the stuff given above, we hope that the students would have understood, "Vector Word Problems and Answers".

Apart from the stuff given in "Vector Word Problems and Answers" if you need any other stuff in math, please use our google custom search here. WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6