Download App

Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra1 Mark
MCQ
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 $\vec{b}, \vec{a} \times \vec{b}=\vec{b} \times \vec{a}$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason $(R)$ is the correct explanation of the Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true, but Reason $(R)$ is not the correct explanation of the Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
✓

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If the matrix $\text{P}=\begin{pmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&3\end{pmatrix}$ is a symmetric matrix, then $\text{a}=-\frac{2}{3}$ and $\text{b}=-\frac{2}{3}.$
Reason: If P is a symmetric matrix, then P' = P.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
→
Assertion (A): Domain of $y=\cos ^{-1}(x)$ is $[-1,1]$.
Reason $(R)$ : The range of the principal value branch of $y=\cos ^{-1}(x)$ is $[0, \pi]-\left\{\frac{\pi}{2}\right\}$.
→
Assertion (A) : $x \sin x \frac{d y}{d x}+(x+x \cos x+\sin x)$ $y=\sin x, y\left(\frac{\pi}{2}\right)=1-\frac{2}{\pi} \Rightarrow y=\frac{x-\sin x}{x(1-\cos x)}$
Reason (R) : The differential equation is linear with integrating factor $x(1-\cos x)$.
→
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}1 & 2\\ 2& 3 \end{pmatrix}$ and $\text{B}=\begin{pmatrix}-1&4\\0&5\end{pmatrix}.$ (A + B)2 = A2 + 2AB + B2.
Reason: $\text{AB}\neq\text{BA}.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
→
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: Points A(4, 0, 4), B(1, 2, 3), C(-2, 4, 2) are collinear.
Reason: Three points A, B, C are collinear if AB + BC = AC and AB, BC < AC.
  1. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion.
  2. Both Assertion & Reason are individually true but Reason is not the, correct (proper) explanation of Assertion.
  3. Assertion is true but Reason is false.
  4. Assertion is false but Reason is true.
→
Assertion (A): The area bounded by the parabola $y^2=4 a x$ and the line $x=a$ and $x=4 a$ is $\frac{56 a^2}{3}$ sq. units.
Reason (R) : The area bounded by the parabola $y^2=49 x$ and $y=m x$ is $8 a^2 / 3 m^3$ sq. units.
→
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: Maximum value of z = 11x + 7y, subjectto constraints $2\text{x}+\text{y}\leq6,\text{x}\leq2,\text{x}\geq0,\text{y}\geq0$ will be obtained at (0, 6).
Reason: In a bounded feasible region, it always exist a maximum and minimum value.
  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: Points A(4, 0, 4), B(1, 2, 3), C(-2, 4, 2) are collinear.
Reason: Three points A, B, C are collinear if AB + BC = AC and AB, BC < AC.
  1. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion.
  2. Both Assertion & Reason are individually true but Reason is not the, correct (proper) explanation of Assertion.
  3. Assertion is true but Reason is false.
  4. Assertion is false but Reason is true.
→
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) : Both $\sin x$ and $\cos x$ are decreasing functions in $\left(\frac{\pi}{2}, \pi\right)$.
Reason (R): If a differentiable function decreases in $(a, b)$, then its derivative also decreases in $(a, b)$.
→