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Given the vector a=(2,-1,3), b=(-1,4,2), c=(7,5,λ) coplanar, then the real number λ= A 62/7 B 63/7 C 64/7 D 65/7 I figured it wasn't one of the four answers.
|2 -1 3 |
|-1 4 2 |
|7 5 λ |
=2*4*λ+(-1)*2*7+3*(-1)*5-3*4*7-(-1)*(-1)*λ-2*2*5
=8λ-14-15-84-λ-20
=7λ-133.λ=133/7=19
Given vector a=(1,2) b=(1, enter) c=(3,4) if a+b is coplanar with c, then real number enter=
Equal to two thirds
Vector a=(sin (a /6),1), vector b=(4,4 cosa-root number 3), if vector a⊥ vector b, what is sin (a+4π/3) equal to
Answer:-1/4
According to the title:4sin (a /6)+4 cosa-root number 3=0
After expansion, it is simplified as:(2 roots 3) sina+6 cosa=root 3
I.e. sina +(root 3)* cosa=1/2
While sin (a+4π/3)= sina*cos4π/3+cosa*sin4π/3=(-1/2)*[ sina+(root 3)*cosa ]=-1/4
Vector a=2,1 vector a×vector b=10|vector a+vector b|=5 n=2, the absolute value of vector b is equal to Vector a=2,1 vector a×vector b=10|vector a+vector b|=5,2, the absolute value of vector b is equal to
50=|Vector a+vector b|2=a2+b2+2ab=5+b2+20, b2=25,|b|=5
What is the square of the product of the number of vectors What is the square of the number product of vectors
A·b=|a||b|cosα
So
(A·b)2=|a|2|b|2cos2α
The two vector dot products are equal to -1// Why are they reversed?
It's cosα=-1.
I.e.α=180°
So it's reverse.
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