Find component of c in direction of a and in direction of b

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Reference no: EM131382624

In terms of the standard basis set {i, j, k}, a = 2i - j - 2k, b = 3i - 4 k and c = i - 5 j + 3k.

(i) Find 3a + 2b - 4 c and |a - b|².

(ii) Find |a|, |b| and a · b. Deduce the angle between a and b.

(iii) Find the component of c in the direction of a and in the direction of b.

(iv) Find a×b, b×c and (a×b)×(b×c).

(v) Find a · (b×c) and (a×b) · c and verify that they are equal. Is the set {a, b, c} rightor left-handed?

(vi) By evaluating each side, verify the identity a×(b×c) = (a · c) b - (a · b) c.

Reference no: EM131382624

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