Question

2. Prove that the vectors À = 4ỉ + 3 j +k and B = 12 î + 9 j+ 3 k are
parallel to each other.
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Answer 1

Answer:

Parallel Vectors: For a given set of vectors to be parallel, they must satisfy the proportionality ratio. That is, the two vectors must be proportional to each other.

If 'a' and 'b' are two vectors such that they are parallel, then we can write it as:

→ a = λ(b)

Here, λ is the ratio between 'a' and 'b' vector.

According to the question,

A = 4i + 3j + k

Here the coefficient of x is 4, the coefficient of y is 3, and the coefficient of z is 1.

B = 12i + 9j + 3k

Here the coefficient of x is 12, the coefficient of y is 9, and the coefficient of z is 3.

Dividing the coefficients of x,y & z respectively, we get:

$\rightarrow \dfrac{A}{B} = \dfrac{4}{12} = \dfrac{3}{9} = \dfrac{1}{3} = \lambda$

Since the ratios are equal to each other, the given set of two vectors are parallel. The ratio of their coefficients is 1/3 which is equal to λ.

Hence in standard form we can write it as:

→ A = λ(B)

→ (4i + 3j + k) = (1/3) {12i + 9j + 3k}