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Vector Algebra Ncert Solutions Maths class 12th Maths Class 12th Vector Algebra

23. If $\vec{a}$   and   $\vec{b}$   are two collinear vectors, then which of the following are incorrect:

(A)   $\vec{b}$   = λ $\vec{a}$   for some scalar λ

(B)   $\vec{a}$   = ± $\vec{b}$

(C) The respective components of   $\vec{a}$   and   $\vec{b}$   are proportional.

(D) Both the vectors   $\vec{a}$   and   $\vec{b}$   have same direction, but different magnitudes.

4 Views | Posted 4 months ago

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Answered by

Vishal Baghel | Contributor-Level 10

4 months ago

We know,

If $\vec{a}$ and $\vec{b}$ are two collinear vector, they are parallel.

So,

$\begin{array}{l} \vec{b} = λ \vec{a} \\ I f, λ = \pm 1, t h e n, \vec{a} = \pm \vec{b} \\ I f, \vec{a} = a_{1} \hat{i} + a_{2} \hat{j} + a_{3} \hat{k} \\ \vec{b} = b_{1} \hat{i} + b_{2} \hat{j} + b_{3} \hat{k}, t h e n \\ \vec{b} = λ \vec{a} \\ b_{1} \hat{i} + b_{2} \hat{j} + b_{3} \hat{k} = λ (a_{1} \hat{i} + a_{2} \hat{j} + a_{3} \hat{k}) \\ = (λ a_{1}) \hat{i} + (λ a_{2}) \hat{j} + (λ a_{3}) \hat{k} \\ b_{1} = λ a_{1}, b_{2} = λ a_{2}, b_{3} = λ a_{3} \\ \frac{b_{1}}{a_{1}} = \frac{b_{2}}{a_{2}} = \frac{b_{3}}{a_{3}} = λ \end{array}$

Hence, the respective component are proportional but, vector $\vec{a}$ and $\vec{b}$ can have different direction.

Thus, the statement given in D is incorrect.

The correct answer is D.

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23. If a→ and b→ are two collinear vectors, then which of the following are incorrect: (A) b→ = λ a→ for some scalar λ (B) a→ = ± b→ (C) The respective components of a→ and b→ are proportional. (D) Both the vectors a→ and b→ have same direction, but different magnitudes.

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