Mathematics Crash Course MHT-CET>Chapter 22 - Vectors>Exercise 1>Q 146

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Force $\hat{i} + 2 \hat{j} - 3 \hat{k}, 2 \hat{i} + 3 \hat{j} + 4 \hat{k}$ and $- \hat{i} - \hat{j} + \hat{k}$ are acting at the point $P (0, 1, 2)$ . The moment of these forces about the point $A (1, - 2, 0)$ is

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Important Questions on Vectors

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Mathematics Crash Course MHT-CET>Chapter 22 - Vectors>Exercise 1>Q 147

Let

\vec{a} = - \hat{i} - \hat{k}, \vec{b} = - \hat{i} + \hat{j}

and

\vec{c} = \hat{i} + 2 \hat{j} + 3 \hat{k}

be three given vectors. If

r

is a vector such that

\vec{r} \times \vec{b} = \vec{c} \times \vec{b}

and

\vec{r} \cdot \vec{a} = 0

, then the value of

\vec{r} \cdot \vec{b}

is

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Mathematics Crash Course MHT-CET>Chapter 22 - Vectors>Exercise 1>Q 148

Let

x_{0}

be the point of local maxima of

f (x) = \vec{a} \cdot (\vec{b} \times \vec{c}),

where

\vec{a} = x \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = - 2 \hat{i} + x \hat{j} - \hat{k}

and

\vec{c} = 7 \hat{i} - 2 \hat{j} + x \hat{k} .

Then the value of

\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}

at

x = x_{0}

is:

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Mathematics Crash Course MHT-CET>Chapter 22 - Vectors>Exercise 1>Q 149

The area of a parallelogram whose two adjacent sides are represented by

\vec{a} = 3 \hat{i} + \hat{j} + 2 \hat{k}

and

\vec{b} = 2 \hat{i} - 2 \hat{j} + 4 \hat{k}

is

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Mathematics Crash Course MHT-CET>Chapter 22 - Vectors>Exercise 1>Q 150

Let

\hat{a}

and

\hat{b}

are two non-collinear unit vectors. If

\vec{u} = \hat{a} - (\hat{a} \cdot \hat{b}) \hat{b}

and

\vec{v} = \hat{a} \times \hat{b}

, then

| \vec{v} |

is equal to

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Mathematics Crash Course MHT-CET>Chapter 22 - Vectors>Exercise 1>Q 151

Let there be two points

A

and

B

on the curve

y = x^{2}

in the plane

O X Y

satisfying

\vec{OA}

.

\hat{i} = 1

and

\vec{OB}

.

\hat{i} = - 2

then the length of the vector

2 \vec{OA} - 3 \vec{OB}

is