285. Transform the vector (4,-2,-4) at (1,2,3) into spherical coordinates. a) 3.197i – 2.393j + 4.472k b) -3.197i + 2.393j – 4.472k c) 3.197i + 2.393j + 4.472k d) -3.197i – 2.393j – 4.472k
285. Transform the vector (4,-2,-4) at (1,2,3) into spherical coordinates. a) 3.197i – 2.393j + 4.472k b) -3.197i + 2.393j – 4.472k c) 3.197i + 2.393j + 4.472k d) -3.197i – 2.393j – 4.472k
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Answer: b
Explanation: r = √(x2+y2+z2
) = 3.74
Θ = cos-1
(z/r) = cos-1
(3/3.74) = 36.7⁰
Φ = tan-1
(y/x) = tan-1
(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j +
(-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k
b) -3.197i + 2.393j – 4.472k
Answer: b
Explanation: r = √(x2+y2+z2
) = 3.74
Θ = cos-1
(z/r) = cos-1
(3/3.74) = 36.7⁰
Φ = tan-1
(y/x) = tan-1
(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j +
(-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.
b) -3.197i + 2.393j – 4.472k
Answer: b
Explanation: r = √(x2+y2+z2
) = 3.74
Θ = cos-1
(z/r) = cos-1
(3/3.74) = 36.7⁰
Φ = tan-1
(y/x) = tan-1
(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j +
(-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.
Answer: b
Explanation: r = √(x2+y2+z2
) = 3.74
Θ = cos-1
(z/r) = cos-1
(3/3.74) = 36.70
Φ = tan-1
(y/x) = tan-1
(2/1) = 63.40
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j +
(-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.
-3.197i + 2.393j – 4.472k
Answer: b
Explanation: r = √(x2+y2+z2
) = 3.74
Θ = cos-1
(z/r) = cos-1
(3/3.74) = 36.7⁰
Φ = tan-1
(y/x) = tan-1
(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j +
(-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.
b
Explanation: r = √(x2+y2+z2) = 3.74
Θ = cos-1
(z/r) = cos-1
(3/3.74) = 36.7⁰
Φ = tan-1
(y/x) = tan-1
(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j + (-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.
Answer: b
Explanation: r = √(x2+y2+z2
) = 3.74
Θ = cos-1
(z/r) = cos-1
(3/3.74) = 36.7⁰
Φ = tan-1
(y/x) = tan-1
(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j +
(-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.