Available Questions 57 found Page 1 of 3
Standalone Questions
#1479
Mathematics
Vector Algebra
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
The scalar product of the vector $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$ with a unit vector along sum of vectors $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$ and $\vec{c}=\lambda\hat{i}-2\hat{j}-3\hat{k}$ is equal to 1. Find the value of $\lambda$.
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#1448
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Vector $\vec{r}$ is inclined at equal angles to the three axes x, y and z. If magnitude of $\vec{r}$ is $5\sqrt{3}$ units, then find $\vec{r}$.
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#1447
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $\vec{a}$ and $\vec{b}$ are position vectors of point A and point B respectively, find the position vector of point C on BA produced such that $BC=3BA$.
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Sol:
Sol:
#1434
Mathematics
Vector Algebra
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $\vec{a}$ and $\vec{b}$ are unit vectors inclined with each other at an angle $\theta$, then prove that $\frac{1}{2}|\vec{a}-\vec{b}|=\sin\frac{\theta}{2}$.
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#1433
Mathematics
Vector Algebra
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $\vec{a}+\vec{b}+\vec{c}=\vec{0}$ such that $|\vec{a}|=3, |\vec{b}|=5, |\vec{c}|=7$, then find the angle between $\vec{a}$ and $\vec{b}$.
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#1426
Mathematics
Vector Algebra
VSA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Let $\vec{a}$, $\vec{b}$, $\vec{c}$ be three vectors such that $\vec{a}\cdot\vec{b}=\vec{a}\cdot\vec{c}$ and $\vec{a}\times\vec{b}=\vec{a}\times\vec{c}$, $\vec{a}\ne\vec{0}$. Show that $\vec{b}=\vec{c}$.
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#1425
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find a vector of magnitude 5 which is perpendicular to both the vectors $3\hat{i}-2\hat{j}+\hat{k}$ and $4\hat{i}+3\hat{j}-2\hat{k}$.
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#1419
Mathematics
Vector Algebra
LA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Show that the area of a parallelogram whose diagonals are represented by $\vec{a}$ and $\vec{b}$ is given by $\frac{1}{2}|\vec{a}\times\vec{b}|$. Also find the area of a parallelogram whose diagonals are $2\hat{i}-\hat{j}+\hat{k}$ and $\hat{i}+3\hat{j}-\hat{k}$.
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#1381
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $\vec{a}$ and $\vec{b}$ are two non-collinear vectors, then find x, such that $\vec{\alpha}=(x-2)\vec{a}+\vec{b}$ and $\vec{\beta}=(3+2x)\vec{a}-2\vec{b}$ are collinear.
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#1378
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $\vec{\alpha}$ and $\vec{\beta}$ are position vectors of two points P and Q respectively, then find the position vector of a point R in QP produced such that $QR=\frac{3}{2}QP$.
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#1377
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
A vector $\vec{a}$ makes equal angles with all the three axes. If the magnitude of the vector is $5\sqrt{3}$ units, then find $\vec{a}$.
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Sol:
Sol:
#1367
Mathematics
Vector Algebra
SA
UNDERSTAND
2025
AISSCE(Board Exam)
Competency
3 Marks
During a cricket match, the position of the bowler, the wicket keeper and the leg slip fielder are in a line given by $\vec{B}=2\hat{i}+8\hat{j}$, $\vec{W}=6\hat{i}+12\hat{j}$ and $\vec{F}=12\hat{i}+18\hat{j}$ respectively. Calculate the ratio in which the wicketkeeper divides the line segment joining the bowler and the leg slip fielder.
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#1361
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Find a vector of magnitude 21 units in the direction opposite to that of $\vec{AB}$ where A and B are the points $A(2,1,3)$ and $B(8,-1,0)$ respectively.
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#1360
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
Competency
2 Marks
Two friends while flying kites from different locations, find the strings of their kites crossing each other. The strings can be represented by vectors $\vec{a}=3\hat{i}+\hat{j}+2\hat{k}$ and $\vec{b}=2\hat{i}-2\hat{j}+4\hat{k}$. Determine the angle formed between the kite strings. Assume there is no slack in the strings.
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#1358
Mathematics
Vector Algebra
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
The diagonals of a parallelogram are given by $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}+3\hat{j}-\hat{k}$. Find the area of the parallelogram.
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#1347
Mathematics
Vector Algebra
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Find a vector of magnitude 4 units perpendicular to each of the vectors $2\hat{i}-\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-\hat{k}$ and hence verify your answer.
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#1294
Mathematics
Vector Algebra
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
2 Marks
In the given figure, ABCD is a parallelogram. If $\vec{AB}=2\hat{i}-4\hat{j}+5\hat{k}$ and $\vec{DB}=3\hat{i}-6\hat{j}+2\hat{k}$ , then find $\vec{AD}$ and hence find the area of parallelogram ABCD.
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#1293
Mathematics
Vector Algebra
VSA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $(\vec{a}+\vec{b})\perp\vec{a}$ and $(2\vec{a}+\vec{b})\perp\vec{b}$ , then prove that $|\vec{b}|=\sqrt{2}|\vec{a}|$.
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#1279
Mathematics
Vector Algebra
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
The position vectors of vertices of $\Delta$ ABC are $A(2\hat{i}-\hat{j}+\hat{k}),$ $B(\hat{i}-3\hat{j}-5\hat{k})$ and $C(3\hat{i}-4\hat{j}-4\hat{k})$ Find all the angles of $\Delta$ Aะะก.
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#1250
Mathematics
Vector Algebra
VSA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Let $\vec{a}$ and $\vec{b}$ be two non-zero vectors. Prove that $|\vec{a}\times\vec{b}|\le|\vec{a}||\vec{b}|$ . State the condition under which equality holds, i.e., $|\vec{a}\times\vec{b}|=|\vec{a}||\vec{b}|$
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Case-Based Questions
CASE ID: #114
Cl: CBSE Class 12
Mathematics
Three friends A, B and C move out from the same location O at the same time in three different directions to reach their destinations. They move out on straight paths and decide that A and B after reaching their destinations will meet up with C at his predecided destination, following straight paths from A to C and B to C in such a way that $\overrightarrow{OA} = \vec{a}$, $\overrightarrow{OB} = \vec{b}$ and $\overrightarrow{OC} = 5\vec{a}-2\vec{b}$ respectively.
SUBJECTIVE
2025
AISSCE(Board Exam)
4 Marks
(i) Complete the given figure to explain their entire movement plan along the respective vectors.
(ii) Find vectors $\vec{AC}$ and $\vec{BC}$.
(iii) (a) If $\vec{a} \cdot \vec{b} = 1$, distance of O to A is 1 km and that from O to B is 2 km, then find the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$. Also, find $|
\vec{a} \times \vec{b}|$.
OR
(iii) (b) If $\vec{a} = 2\hat{i} - \hat{j} + 4\hat{k}$ and $\vec{b} = \hat{j} - \hat{k}$, then find a unit vector perpendicular to $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$.
(ii) Find vectors $\vec{AC}$ and $\vec{BC}$.
(iii) (a) If $\vec{a} \cdot \vec{b} = 1$, distance of O to A is 1 km and that from O to B is 2 km, then find the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$. Also, find $|
\vec{a} \times \vec{b}|$.
OR
(iii) (b) If $\vec{a} = 2\hat{i} - \hat{j} + 4\hat{k}$ and $\vec{b} = \hat{j} - \hat{k}$, then find a unit vector perpendicular to $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$.
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