Question

If a + 2 b and 3a + mb are parallel then the value of m is​

Answer 1

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Answer 2

If vector(a + 2b) and vector (3a + mb) are parallel, then the value of m is ....

solution : when two vectors are parallel then cross product of them must be zero.

here (a + 2b) and (3a + mb) are parallel to each other.

so, (a + 2b) × (3a + mb) = 0

⇒a × (3a + mb) + 2b × (3a + mb) = 0

⇒a × 3a + a × mb + 2b × 3a + 2b × mb = 0

⇒3 (a × a) + m (a × b) + 6(b × a) + mb(b × b) = 0

here a × a = 0 , b × b = 0 , b × a = -a × b

so, 0 + m(a × b) - 6(a × b) + 0 = 0

⇒(m - 6)(a × b) = 0

a × b ≠ 0 so m - 6 = 0 ⇒m = 6

Therefore the value of m is 6