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JEE MATHEMATICS MCQ: ADDITION OF VECTORS

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Analyzing +4 | -1

For any vector

\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}

, with

10\left|a_i\right|<1, i=1,2,3

, consider the following statements:

(A) :

\max \left\{\left|a_1\right|,\left|a_2\right|,\left|a_3\right|\right\} \leq|\vec{a}|

(B) :

|\vec{a}| \leq 3 \max \left\{\left|a_1\right|,\left|a_2\right|,\left|a_3\right|\right\}

View answer and explanation

Correct option: C

Both

(A)

and

(B)

are true

Option C is correct. Statement A is true because the magnitude of a vector is always greater than or equal to the magnitude of any of its components. Statement B is also true because the magnitude of a vector is less than or equal to 3 times the maximum of the absolute values of its components.

More Questions from ADDITION OF VECTORS

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

\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}

\mathbf{d}

a

unit vector such that

\mathbf{a} \cdot \mathbf{d}=0=(b \mathbf{c}

\mathbf{d}

is equal to
A vector

{\mathbf{\vec a}}

2\;p

and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense, if this respect to new system

{\mathbf{\vec a}}

p + 1

\vec{a}, \vec{b}

\vec{c}

are three mutually perpendicular unit vetors and

\vec{d}

is a unit vector which makes equal angles with

\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}

\overrightarrow{\mathrm{c}}

then the value of

|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|^2

The non-zero vectors are

\vec{a}, \vec{b}

\vec{c}

\vec{a}=8 \vec{b}

\vec{c}=-7 \vec{b}

. Then the angle between

\vec{a}

\vec{c}

is If the vectors

2 \mathbf{i}+\mathbf{j}-\mathbf{k},-\mathbf{i}+2 \mathbf{j}+\lambda \mathbf{k}

-5 \mathbf{i}+2 \mathbf{j}-\mathbf{k}

ar coplanar, then the value of

\lambda

is equal The medium

AD

of the triangle

ABC

E,\;BE

AC

F

AF:AC =