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Vector a=(cosx, sinx), vector (b=-√3,-1), then what is the maximum and minimum values of 2a-b?
A =(cosθ, sinθ), so |a|= root (cosθ+ sinθ)=1
B=(√3,1), so |b|=root ((√3)+(-1))=2
A* b= cosθ*(√3)+ sinθ*(-1)=(√3) cosθ-sinθ=2 cos (/6)
|2A-b|
=(2A-b)
=4A-4a*b+b
=4|A|-4a*b+|b|
=4-8Cos (/6)+4
=8(1-Cos (/6))
Because,-1
In triangle ABC, angle C equals 90 degrees, vector AB equals (k,1), vector AC equals (2,3), then k is?
Vector CB = Vector AB - Vector AC =(k-2,-2)
Vector CB Vertical Vector AC
Then vector CB * vector AC=0
I.e.(k-2,-2)*(2,3)=0
I.e.2k-4-6=0
Solution k=5
Given A (-1,1), B (1,2), C (3,1/2), then the vector AB? Vector AC equals: A.2/5 B.15/2 C.-5/2 D-15/2(to... Given A (-1,1), B (1,2), C (3,1/2), then the vector AB? Vector AC equals: A.2/5 B.15/2 C.-5/2 D-15/2(to be detailed)
Vector AB=(1,2)-(-1,1)=(2,1)
Vector AC=(3,0.5)-(-1,1)=(4,-0.5)
You require quantity product, equal to 2*4-1*0.5=7.5=15/2, choose B
Given vectors a=(1,2), b=(-3,2), when k is: 1 Vector ka+b is perpendicular to a-3b;2 vector ka+b is parallel to a-3b? Same or opposite?
(1) Ka+b=(k-3,2k+2) a-3b=(10,-4)(ka+b)*(a-3b)=0 10(k-3)-4(2k+2)=0k=19(2) ka+b=(k-3,2k+2) a-3b=(10,-4)(ka+b)//(a-3b)-4(k-3)-10(2k+2)=0k=-1/3 ka+b=(-3/10,4/3) a-3b=(10,-4) ka+b=λ(a-3b)λ
Let vector a=(2k+2,3) and vector b=(8, k+2). If vector a is in the same direction as vector b, then the value of k is RT Detailed Explanation Let vector a=(2k+2,3) and vector b=(8, k+2). If vector a is in the same direction as vector b, then the value of k is RT Details
If a vector is in the same direction as b vector, then (a)= x (b), i.e.:
2K +2=8x
3=X*(k+2)
Solution k=-5 or k=2
If a vector is in the same direction as b vector, then (a)= x (b), i.e.:
2 K +2=8 x
3=X*(k+2)
Solution k=-5 or k=2
Given the vector a=(1, k), b=(2,6), and a//b.(1) Find the value of k
Because a//b, x1y2=x2y1, i.e.2k=6*1, k=3.
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