(a) Consider the vectors a - -2i + 10j + 11k and b - 1i - 2j + 2k, where i, j, and k are mutually-perpendicular unit vectors forming a right-handed system. Calculate: (b) Let the vectors a and b in part (a) of this question represent the position vectors of a 2 kg point mass and a 4 kg point mass respectively (where the units of distance are considered to be subsumed within i, j, and k). Calculate where a third point mass of 3 kg would need to be positioned to make the centre of mass of the system lie at the origin. (c) Prove, by writing out in component form, that ) c (e x d) - 0. (i) (c x d) xe - (c e)d - (d-e)c.

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A: Given: The vectors u = 2i - 5j, v = -3i + 7j, and w = -i - 6j

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A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

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A: The complete solutions are given below

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Q: 5. Express the vector having magnitude 7, and direction 13 degrees (when drawn in standard…

A: Solve the following

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Q: The ________ ________ of two vectors yields a scalar, rather than a vector.

A: Given as  The ________ ________ of two vectors yields a scalar, rather than a vector.

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Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

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A: Introduction :

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A: To check whether the vectors are linearly dependent or linearly independent.

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Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar 5v.

A: Consider the given vectors u=2i-5j , v=-3i+7j , w=-i-6j

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Q: Find a non-zero vector perpendicular to the vectors -2 and ü = 2 ||

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Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar lul.

A: Given vectors are u=2i-5j, v=-3i+7j and w=-i-6j. To find: u  Solution: Magnitude of a vector is…

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A: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

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Q: Find a vector orthogonal to the vectors ā = and 5=.

A: Recall:  Vector orthogonal to the vectors a→ and b→ is a→×b→a→×b→ We have, a→=1,2,3, b→=1,0,1