Classify the following as scalar and vec | Class 12 Mathematics Chapter Vector Algebra, Vector Algebra NCERT Solutions

In Figure, identify the following vectors.

(i) Coinitial (ii) Equal (iii) Collinear but not equal

Classify the following measures as scalars and vectors.

(i) 10 kg (ii) 2 metres north-west (iii) 40°

(iv) 40 watt (v) 10^–19 coulomb (vi) 20 m/s²

Answer the following as true or false.

 \begin{align}(i) \overrightarrow{a}\;  and\; \overrightarrow{-a}\; are\; collinear.\end{align}

(ii) Two collinear vectors are always equal in magnitude.

(iii) Two vectors having same magnitude are collinear.

(iv) Two collinear vectors having the same magnitude are equal.

Represent graphically a displacement of 40 km, 30° east of north.

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

(i) f : R → R defined by f(x) = 3 – 4x

(ii) f : R → R defined by f(x) = 1 + x² 

 Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.

 Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Show that the function f : R_* → R_* defined by f(x) = 1/x is one-one and onto,where R_* is the set of all non-zero real numbers. Is the result true, if the domain R_* is replaced by N with co-domain being same as R_* ? 

 Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof. 

 Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Letbe a function defined as. The inverse of f is map g: Range

(A)  

(B) 

(C)  

(D)