Download App

Vector Algebra — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra1 Mark
Question
Assertion (A): For two hon-zero vectors $\vec{a}$ and $b , \vec{a} \cdot b = b \cdot \vec{a}$.
Reason (R): For two non-zero vectors $\vec{a}$ and $\vec{b}, \vec{a} \times \vec{b}=\vec{b} \times \vec{a}$.
✓

Answer

Assertion (A) is true but reason $( R )$ is false. As, $\vec{a} \times \vec{b}=-\vec{b} \times \vec{a}$.

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 "Assertion (A) & Reason (B) MCQ" from Vector Algebra→Vector Algebra — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Assertion (A): For any symmetric matrix A, B'AB is a skew-symmetric matrix.
Reason (R): A square matrix P is skew-symmetric if P'$P^{\prime}=-P$.
→
Assertion (A): The relation $R=\{(x, y):(x+y)$ is a prime number and $x, y \in N\}$ is not a reflexive relation.
Reason (R) : The number ' $2 n$ ' is composite for all natural numbers $n$.
→
Assertion (A): If x is real, then the minimum value of $x ^2-8 x +17$ is 1
Reason (R): If f"(x) > 0 at a critical point, then the value of the function at the critical point will be the minimum value of the function.
→
Let $A$ and $B$ be two events associated with an experiment such that $P(A \cap B)=P(A) P(B)$.
Assertion (A) : $P(A \mid B)=P(A)$ and $P(B \mid A)=$ $P(B)$
Reason (R): $P(A \cup B)=P(A)+P(B)$.
→
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The linear programming problem,maximize z = 2x + 3y subject to constraints $\text{x}+\text{y}\leq4,\text{x}\geq0,\text{y}\geq0$ It gives the maximum value of Z as 8 .
Reason: To obtain maximum value of Z, we need to compare value of Zat all the corner points of the feasible region.
  1. A is true, R is true: R is a correct explanation for A.
  2. A is true,R is true; R is not a correct explanation for A.
  3. A is true: R is false.
  4. A is false: R is true.
→
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Three points with position vectors $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ are collinear if  $\vec{\text{a}}\times\vec{\text{b}}+\vec{\text{b}}\times\vec{\text{c}}+\vec{\text{c}}\times\vec{\text{a}}=\vec{0}$
Reason: If $\overrightarrow{\text{AB}}.\overrightarrow{\text{AC}}.=0,$ then $\overrightarrow{\text{AB}}\bot\overrightarrow{\text{AC}}.$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
→
Assertion $(A):$ The lines $\vec{r}=\vec{a}_1+\lambda \vec{b}_1$ and $\vec{r}=\vec{a}_2+\mu \vec{b}_2$ are perpendicular, when $\vec{b}_1 \cdot \vec{b}_2=0$.
Reason $(R):$ The angle $\theta$ between the lines $\vec{r}=\vec{a}_1+\lambda \vec{b}_1$ and $\vec{r}=\vec{a}_2+\mu \vec{b}_2$ is given by $\cos \theta=\frac{\vec{b}_1 \cdot \vec{b}_2}{\left|\vec{b}_1\right|\left|\vec{b}_2\right|}$.
→
Assertion (A) : Let $f:(e, \infty) \rightarrow R$ defined by $f(x)=\log (\log (\log x))$ is bijective.
Reason (R) : A function $f$ will be bijective if $f$ is both one-one and onto.
→
Let R be any relation in the set A of human beings in a town at a particular time.
Assertion (A): If $R=\{(x, y): x$ is wife of $y\}$, then $R$ is reflexive.
Reason (R): If $R=\{(x, y): x$ is father of $y\}$, then R is neither reflexive nor symmetric nor transitive.
→
 Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as : Assertion : Matrix $\text{A}=\begin{pmatrix}1 & 2 \\ -2 & 1\end{pmatrix},$ satisfies the equation $x2 - 2x + 5I = 0,$ then $A$ is invertible.
Reason: If a square matrix satisfies the equation $a_nX^n + a_{n-1}X^{n-1} + .... + a_1X + a_nI^z = 0$ and $\text{a}_\text{n}\neq0,$ Then $A$ is invertible.
→