Download App

Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
If $\bar{c}=2 \bar{a}-3 \bar{b}$ and $2 \bar{c}=3 \bar{a}+4 \bar{b}$, then $\bar{c}$ and $\bar{a}$ are
  • ✓
    like parallel vectors
  • B
    unlike parallel vectors
  • C
    at right angles
  • D
    none of these
✓

Answer

Correct option: A.
like parallel vectors
(A) Given $\overline{ c }=2 \overline{ a }-3 \overline{b}$ ...(i)
and $2 \overline{ c }=3 \overline{ a }+4 \overline{b}$ ...(ii)
Multiplying (i) by 4 and (ii) by 3 and adding,
we get
$10 \overline{ c }=17 \overline{ a }$
$\Rightarrow \overline{ c }=\frac{17}{10} \overline{ a }$
Since $\bar{c}$ and $\bar{a}$ are in the same direction.
$\therefore \quad \overline{ c }$ and $\overline{ a }$ are like parallel vectors.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Vectors→Vectors — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The relation $S$ defined on the set $R$ of all real number by the rule $aSb$ iff $a  ≥  b$ is:
→
If a line lies in the octant OXYZ and it makes equal angles with the axes, then
→
A bag contains $5$ red and $3$ blue balls are drawn at random without replacement, then the probability of getting exactly one red ball is.
→
$\hat{ i } \cdot(\hat{ j } \times \hat{ k })+\hat{ j } \cdot(\hat{ i } \times \hat{ k })+\hat{ k } \cdot(\hat{ i } \times \hat{ j })$ is equal to
→
The angle between the straight lines $x^2+4 x y+y^2=0$ is
→
In a triangle ABC , $\frac{2 \cos A}{a}+\frac{\cos B}{b}+\frac{2 \cos C}{c}=\frac{a}{b c}+\frac{b}{c a}$, then the value of angle A is
→
If two lines $a x^2+$$2 h x y+b y^2$$=0$ are equally inclined with co-ordinate axes, then
→
The value of $f(0)$, so that the function $\text{f(x)}=\frac{(27-2\text{x})^\frac{1}{3}-3}{9-3(243+5\text{x})^\frac{1}{5}}$ is continuous, is given by:
→
If $\sin^{-1}\text{x}-\cos^{-1}\text{x}=\frac{\pi}{6},$ then $x =$
→
Bacterial increases at the rate proportional to the number present. If original number $M$ doubles in 3 hours, then number of bacteria will be $4 M$ in
→