Download App

Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors1 Mark
MCQ
If $|\bar{a}|=2,|\bar{b}|=3|\bar{c}|=4$ then $[\bar{a}+\bar{b} \bar{b}+\bar{c} \bar{c}-\bar{a}]$ is equal to
  • A
    24
  • B
    -24
  • ✓
    0
  • D
    48
✓

Answer

Correct option: C.
0
$[\bar{a}+\bar{b} \bar{b}+\bar{c} \bar{c}-\bar{a}]=0$

$Explanation:$
$(\bar{a}+\bar{b}) \cdot[(\bar{b}+\bar{c}) \times(\bar{c}-\bar{a})] \\
=\bar{b} \times \bar{c}-\bar{b} \times \bar{a}+\bar{c} \times \bar{c}-\bar{c} \times \bar{a} \\
=(\bar{a}+\bar{b}) \cdot[\bar{b} \times \bar{c}-\bar{b} \times \bar{a}-\bar{c} \times \bar{a}] \\
=\bar{a} \cdot(\bar{b} \times \bar{c})-\bar{a} \cdot(\bar{b} \times \bar{a})-\bar{a} \cdot(\bar{c} \times \bar{a})+\bar{b} \cdot(\bar{b} \times \bar{c})-\bar{b} \cdot(\bar{b} \times \bar{a})-\bar{b} \cdot(\bar{c} \times \bar{a}) \\
=\bar{a} \cdot(\bar{b} \times \bar{c})+0+0+0+0-\bar{b} \cdot(\bar{c} \times \bar{a}) \\
=(\bar{a} \bar{b} \bar{c})-(\bar{a} \bar{b} \bar{c})=0$

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

If A and B are square matrices of the same order and $AB =3 I$, then $A ^{-1}$ is equal to
→
$\mathrm{f}(x)=\left\{\begin{array}{cc}\mathrm{k} x^2 ; & 0 \leq x \leq 2 \\0 ; & \text { otherwise }\end{array}\right.$ is a p.d.f. of $X$.
The value of $k$ is
→
Dual of the statement $(p \wedge q) \vee \neg q \equiv p \vee \neg q$ is
→
Which of the following is a homogeneous differnetial equation?
→
Let $*$ be a binary operation on $N$ defined by $a * b = a + b + 10$ for all $a, b \in N.$ The identity element for $*$ in $N$ is:
→
If in a triangle, the are in A.P. and $b: c=\sqrt{3}: \sqrt{2}$ then $A$ is equal to
→
The derivative of $f(\tan x)\ \text{w.r.t.} \ g(\sec x)$ at $x=\frac{\pi}{4}$, where $f^{\prime}(1)=2$ and $g^{\prime}(\sqrt{2})=4$, is
→
If A is an $3 \times 3$ non-singular matrix such that $A A^{\prime}=A^{\prime} A$ and $B=A^{-1} A^{\prime}$, then $B B^{\prime}$ equals
→
If m and n are the order and degree of the differential equation $(\text{y}_{2})^{5}+\frac{4(\text{y}_{2})^{3}}{\text{y}^{3}}+\text{y}^{3}=\text{y}_{3}=\text{x}^{2}-1$, then
→
If $X \sim B(n, P)$ and $E(X)=12, \operatorname{Var}(X)=4$, then the value of $n$ is $\ldots . .$.
→