(D) Let $r = xi + yj + zk$. Given $r \cdot i = r \cdot j = r \cdot k$, we have $x = y = z$. Let $x = y = z = a$. Then $r = a(i + j + k)$. Given $|r| =

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(D) Let $r = xi + yj + zk$. Given $r \cdot i = r \cdot j = r \cdot k$, we have $x = y = z$. Let $x = y = z = a$. Then $r = a(i + j + k)$. Given $|r| = 3$, we have $\sqrt{a^2 + a^2 + a^2} = 3$. $\sqrt{3a^2} = 3 \Rightarrow |a|\sqrt{3} = 3$. $|a| = \frac{3}{\sqrt{3}} = \sqrt{3}$. Thus, $a = \pm \sqrt{3}$. Therefore, $r = \pm \sqrt{3}(i + j + k)$.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

Easy

If $r \cdot i = r \cdot j = r \cdot k$ and $|r| = 3$, then $r = $

A
$\pm 3(i + j + k)$
B
$\pm \frac{1}{3}(i + j + k)$
C
$\pm \frac{1}{\sqrt{3}}(i + j + k)$
D
$\pm \sqrt{3}(i + j + k)$

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Class 12

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Vector Algebra

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Basic , Modulus and Algebra of vectors

For any two vectors $\vec{a}$ and $\vec{b}$,which of the following statements is true?

Easy

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If vectors $a$ and $b$ represent two consecutive sides of a regular hexagon,then the vectors representing the remaining four sides in order are:

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If $a$ and $b$ are two non-collinear vectors and the vector $a+b$ bisects the angle between $a$ and $b$,then

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Classify the following measure as a scalar or a vector: $20 \, m/s^{2}$.

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If non-zero vectors $\vec{a}$,$\vec{b}$,and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} = -7\vec{b}$,find the angle between $\vec{a}$ and $\vec{c}$.

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If $r \cdot i = r \cdot j = r \cdot k$ and $|r| = 3$, then $r = $

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For any two vectors $\vec{a}$ and $\vec{b}$,which of the following statements is true?

If vectors $a$ and $b$ represent two consecutive sides of a regular hexagon,then the vectors representing the remaining four sides in order are:

If $a$ and $b$ are two non-collinear vectors and the vector $a+b$ bisects the angle between $a$ and $b$,then

Classify the following measure as a scalar or a vector: $20 \, m/s^{2}$.

If non-zero vectors $\vec{a}$,$\vec{b}$,and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} = -7\vec{b}$,find the angle between $\vec{a}$ and $\vec{c}$.

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