Question

a = 2i + 5j +k and b = 4i + mj + nk are collinear vectors, then find m and n.

Answer 1

Answer : ⇒   m = 10       And     n =   2

Given that

⇒ the vectors 2i + 5j +k and 4i + mj + nk are collinear vectors.

Collinear means the vectors lying on the Same Line.

So the vectors can be

• Parallel
• Anti-parallel

In both cases, the ratio of their respective components will be Equal.

So we have

                        4i + mj + nk    &

                         2i + 5j +k

Comparing both, we get

       4/2 = m/5 = n/1

          2 = m/5 = n/1

⇒  2 = m/5   And   2 = n/1

⇒ m/5 = 2   And    n/1 = 2

⇒  m = 5 (2)     And   n = 2

⇒   m = 10        And     n =   2

Answer 2

Answer:

Step-by-step explanation:

Answer : ⇒ m = 10 And n = 2

Given that

⇒ the vectors 2i + 5j +k and 4i + mj + nk are collinear vectors.

Collinear means the vectors lying on the Same Line.

So the vectors can be

Parallel

Anti-parallel

In both cases, the ratio of their respective components will be Equal.

So we have

4i + mj + nk &

2i + 5j +k

Comparing both, we get

4/2 = m/5 = n/1

2 = m/5 = n/1

⇒ 2 = m/5 And 2 = n/1

⇒ m/5 = 2 And n/1 = 2

⇒ m = 5 (2) And n = 2

⇒ m = 10 And n = 2