Ex 10.1, 5 Answer the following as true or false. (i) 𝑎 ⃗ and − 𝑎 ⃗ are collinear.Two vectors are collinear if they are parallel to line the same line.
Here, 𝑎 ⃗ and −𝑎 ⃗ are parallel to line 𝑚 ⃗
So, 𝑎 ⃗ and −𝑎 ⃗ are collinear.
Hence, True.
Ex 10.1, 5 Answer the following as true or false. (ii) Two collinear vectors are always equal in magnitude.Two vectors are collinear, if they are parallel to the same line.
Here, 𝑎 ⃗ and 𝑏 ⃗ are parallel to 𝑚 ⃗
Hence, collinear.
But, 𝑎 ⃗ and 𝑏 ⃗ are not equal in magnitude.
Thus, False.
Ex 10.1, 5 Answer the following as true or false. (iii) Two vectors having same magnitude are collinear.Two or more vectors are collinear if they are parallel to the same line
𝑎 ⃗ and 𝑏 ⃗ are equal in magnitude but not parallel to the same line
So, 𝑎 ⃗ and 𝑏 ⃗ are not collinear
Hence, False.
Ex 10.1, 5 Answer the following as true or false. (iv) Two collinear vectors having the same magnitude are equal.Two or more vectors are collinear if they are parallel to the same line.
𝑎 ⃗ and 𝑏 ⃗ are parallel to 𝑚 ⃗ , and thus collinear.
Also 𝑎 ⃗ and 𝑏 ⃗ have the same magnitude.
But they have opposite directions.
Now,
Two or more vectors are equal if they have the
Same Magnitude
Same Direction
Since, 𝑎 ⃗ and 𝑏 ⃗ have opposite directions, they are collinear vectors having the same magnitude but are not equal
Hence, False

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.