向量工課(求強大的人賜教)

2014-11-19 10:50 pm

if a = 3i-4j+2k , b=2i-2j+3k , c=-6i+8j-4k , find axb , bxc , cxa , what is special about a , b , c ?

Answer the following question
Is a．b vector ?
Can a．b be negative , if yes , what is the criteria ?
If ab=lallbl , what is special about a and b ?
If a．b =0 , what is special about a and b ?
If axb =0 , what is special about a and b ?

Vector s R and S are directed towards east and north east , let RxS=T
find the direction of T
find the direction of TxR
if lRl = lSl = 2 , what is lTl ?
if lRl = lRl 3 , find the value of R．S
if lRl = lSl = 5 , find the value of S．(TxR)

回答 (1)

Eddie

2014-11-21 2:58 am

✔ 最佳答案

a = 3i-4j+2k , b=2i-2j+3k , c=-6i+8j-4k
axb =[(-4×3)-(-2×2)]i+[(2×2)-(3×3)]j+[(3×-2)-(2×-4)]k=-8i-5j+2k
bxc =[(-2×-4)-(3×8)]i+[(3×-6)-(-4x2))j+[(2×8)-(-6×-2)]k=-16i-10j+4k=2(-8i-5j+2k)
cxa =[(8×2)-(-4×-4)]i+[(-6×-4)-(8×3)]j+[(-6×-4)-(8×3)]k=0i+0j+0k
The magnitude of bxc is twice that of axb, cxa is a zero vector.
Vector a and c are in opposite direction (180°), vector c has a magnitude twice that of vector a.

a • b = ax × bx + ay × by + az × bz
= 3 × 2 + (-4) × (-2) + 2 × 3 = 20

a • b can be negative if the angle between the two vectors is greater than 90°.
If ab=lallbl [i.e. cos(θ)=1], the two vectors are in the same direction (i.e. zero angle in between them).
If a•b =0 [i.e. cos(θ)=0], the two vectors are perpendicular to each other (i.e. 90° in between them).
If axb =0 [i.e. sin(θ)=0], the two vectors are in the same direction (i.e. zero angle in between them).

For the second part, should "if lRl = lRl 3 , find the value of R．S" be "if lRl = lSl = 3 , find the value of R．S"?

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