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Two adjacent sides of a parallelogram are represented by the two vectors, $\hat{i} + 2 \hat{j} + 3 \hat{k}$ and $3 \hat{i} - 2 \hat{j} + \hat{k}$ . What is the area of the parallelogram?

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Important Questions on Scalars and Vectors

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 56

Three vectors satisfy the relation,

\vec{A} \cdot \vec{B} = 0

and

\vec{A} \cdot \vec{C} = 0

. Then,

\vec{A}

is parallel to,

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 57

The component of a vector

r

along

x

-axis will have a maximum value if,

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 58

|\vec{A} \times \vec{B}| = \sqrt{3} \vec{A} \cdot \vec{B}

, then the value of

|\vec{A} + \vec{B}|

is,

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 59

The sum of magnitude of two forces is

25 N

. The resultant of these forces is normal to the smaller force and has a magnitude of

10 N

. Then, the two forces are,

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 60

Consider a particle on which constant forces,

{\vec{F}}_{1} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) N

and

{\vec{F}}_{2} = (4 \hat{i} - 5 \hat{j} - 2 \hat{k}) N

act together resulting in a displacement from position,

{\vec{r}}_{1} = (20 \hat{i} + 15 \hat{j}) cm

{\vec{r}}_{2} = (7 \hat{k}) cm

. The total work done on the particle is,

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 61

A particle moves from a point

(- 2 \hat{i} + 5 \hat{j})

(4 j + 3 \hat{k})

when a force of

(4 \hat{i} + 3 \hat{j}) N

is applied. How much work has been done by the force?

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 62

A force,

\vec{F} = - K (y \hat{i} + x \hat{j})

(where,

K

is a positive constant) acts on a particle moving in the

x - y

plane. Starting from the origin, the particle is taken along the positive

x

-axis to the point

(a, 0)

and then parallel to the

y

-axis to the point

(a, a)

. The total work done by the force

\vec{F}

on the particle is,

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MHT-CET TRIUMPH Physics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Scalars and Vectors>Competitive Thinking>Q 63

The vector sum of two forces is perpendicular to their vector difference. In that case, the forces,

Two adjacent sides of a parallelogram are represented by the two vectors, i^+2j^+3k^ and 3i^-2j^+k^. What is the area of the parallelogram?

Important Questions on Scalars and Vectors

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Two adjacent sides of a parallelogram are represented by the two vectors, $\hat{i} + 2 \hat{j} + 3 \hat{k}$ and $3 \hat{i} - 2 \hat{j} + \hat{k}$ . What is the area of the parallelogram?