Vectors a, b, c make 60^(circ) angles with each other. |a|=4, |b|=2, |c|=6. Find the length of p=a+b+c.

Hayley Bernard 2022-07-17 Answered
Vectors a, b, c make 60 angles with each other. | a | = 4, | b | = 2 , | c | = 6. Find the length of p=a+b+c.
The only way I can think of a, b and c having 60 angles with each other is that they form a vertex of a tetrahedron. Then, I can find |a+b| or |b+c| or |a+c| using the law of cosines. But then I can't find |p|, because I don't know the angle between the vector I have found and the remaining one.
I would like to get some hints or clues how to solve this, thanks in advance.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

eishale2n
Answered 2022-07-18 Author has 15 answers
I would square the given sum:
p 2 = ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 a b + 2 b c + 2 c a
This is equal
| a | 2 + | b | 2 + | c | 2 + 2 | a | | b | cos ( π / 3 ) + 2 | b | | c | cos ( π / 3 ) + 2 | a | | c | cos ( π / 3 )
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-05-29
Which of the following expressions are meaningful? Which are meaningless? Explain.
a) (ab)c
(ab)c has ? because it is the dot product of ?.
b) (ab)c
(ab)c has ? because it is a scalar multiple of ?.
c) |a|(bc)
|a|(bc) has ? because it is the product of ?.
d) a(b+c)
a(b+c) has ? because it is the dot product of ?.
e) ab+c
ab+c has ? because it is the sum of ?.
f) |a|(b+c)
|a|(b+c) has ? because it is the dot product of ?.
asked 2021-05-17
Find the scalar and vector projections of b onto a.
a=(4,7,4),b=(3,1,1)
asked 2021-05-29

Find the vector and parametric equations for the line segment connecting P to Q.
P(0, - 1, 1), Q(1/2, 1/3, 1/4)

asked 2021-02-11
Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in M2×4 with the property that FA = 0 (the zero matrix in M3×4). Determine if H is a subspace of M2×4
asked 2022-07-16
I have a linear map R α = ( c o s α s i n α s i n α c o s α ) and the question goes like, how does R α transform a vector?
Can someone please help me?
asked 2022-08-24
How to find the position vector for the point of intersection of a line and the perpendicular line through a point C
How could I find the exact coordinates of the point N for example which is the point of intersection of the line L = ( 0 1 2 ) + t ( 3 2 3 ) and a perpendicular line that passes through a point C(1,2,3) not on the line.
What I have done so far is find the value of point N in terms of t to find the vector C N :
N ( 3 t 2 t 1 3 t + 2 )
C N = ( 3 t 2 t 1 3 t + 2 ) ( 1 2 3 )
= ( 3 t 1 2 t 3 3 t 1 )
After this I made the scalar product eual zero:
C N ( 3 2 3 ) = 0
With this I find that,
t = 6 11
But my textbook says that
t = 5 11
Can anyone confirm which answer for t is right and if it is t = 5 11 then what did I do wrong?
asked 2022-09-05
Let v 1 = ( 1 1 0 0 ) , v 2 = ( 0 1 1 0 ) , v 3 = ( 0 0 1 1 ) , v 4 = ( 2 0 0 1 ) R 4 vectors.
Show that every v R 4 × 1 can be written as vectors ( v 1 , v 2 , v 3 , v 4 ) linear combination.
My attempt:
[ 1 0 0 2 v 1 1 1 0 0 v 2 0 1 1 0 v 3 0 0 1 1 v 4 ]
Where do I go from here? Every input is appreciated.

New questions