Collinearity Of two vectors

Chapter 10 Class 12 Vector Algebra
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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 