Prove that vector a =-2i+3j+k and vector b= 2i-3j-k are parller to each other
Answers
Answer:
Therefore you have
v1→=2i^+3j^−k^
v2→=4i^+6j^+xk^
Now v1→ is parallel to v2→ implies
v1→=kv2→ where k is a scale factor.
therefore we have
2=4k
3=6k
−1=xk
From the first two equations we have
k=0.5
substituting into the third equation we have
−1=0.5x which then gives x=−2
Two vectors a and b are parallel if they point in the same direction. It stands to reason that they are multiples of each other (you and scale one into the other)
all you need to do them is study the following equation:
λa=b
Using your question, a=(2,3,−1) and b=(4,6,x) , you will get three simultaneous equations
2λ=4
3λ=6
−λ=x
the first two tell you that λ=2 , and plugging that into the last one tells you that x=−2 .
If A vector = 3i^+4j^ and B vector = 7i^+24j^, what is the vector having the same magnitude as B vector and parallel to A vector?
If vectors A=2i+2j+3k and B=3i+6k+nk are perpendicular to each other then what the value of n?
For what value of 'a' the vector 2i-3j+4k and ai+6j-8k are perpendicular to each other?
Two vectors are parallel if and only if they are scalar multiples of one another.
Let
A⃗ =2i+3j−k⟹2A⃗ =4i+6j−2k
B⃗ =4i+6j+xk
4i+6j−2k=4i+6j+xk
⟹x=−2
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If the two given vectors 2i + 3j - k and 4i + 6j + x k are parallel then, we must have the coefficients of i, j, k comparable, that is ;
2/4 = 3/6 = -1/x ==> x = - 2 .
Vectors can be written as (2,3,-1) and (4,6,x) or 2*(2,3,x/2)
For the vectors to be parallel, the components must be proportional, hence in this case x/2 = -1, therefore x = -2