Find the transformation Av which aligns a given vector V = ai + bj + ck with the vector k along the positive z axis.

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written 7.2 years ago by

teamques10 ★ 70k

• modified 3.9 years ago

Mumbai university > mechanical engineering > sem 7 > cad/cam/cae

Marks: 10M

Year: May 2016

Difficulty: Medium

cad cam cae

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written 7.2 years ago by

teamques10 ★ 70k

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The given vector is <html><body>

V = a_i + b_j + c_k

</body></html>

a=0 , b=1 , c=1

also enter image description here

Step 1: Rotation of vector V about X-axis by an angle θ=+ θ1 {+ve indicates CCW}

Now, <html><body>

V₁ = b_j + c_k

</body></html>

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Now, the rotational matrix about x-axis is,

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On substituting the values of sin θ1 and cosθ1, we get,

enter image description here

Step 2: Rotate vector V1 about Y-axis by an angle of θ=- θ2 So as to consider with z-axis

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Now, rotational matrix about y-axis is,

enter image description here

Now, combined transformation, [Av] = [Rx] [Ry]

enter image description here

This is the matrix [Av] which aligns a given vector <html><body>

V = a_i + b_j + c_k

</body></html> with the vector k along positive z-axis

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