If a-b and a-b are perpendicular and b-3- -4- -2k- then - a - is equal to

The correct option is C √( 29 ) Given, (a+b) and (a b) are perpendicular ∴ (a+b).(a b)=0 ⇒ a^2 b^2=0 ⇒| a | =| b | ...

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Standard XII

Mathematics

Applications of Dot Product

If a+b and ...

Question

If $a + b$ and $a - b$ are perpendicular and $b = 3^i - 4^j + 2^k$ , then $| a |$ is equal to

\sqrt{41}

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\sqrt{39}

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\sqrt{19}

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\sqrt{29}

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\sqrt{31}

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Solution

The correct option is C $\sqrt{29}$
Given,
$(a + b)$ and $(a - b)$ are perpendicular
$∴$ $(a + b) . (a - b) = 0$
$\Rightarrow$ $a^{2} - b^{2} = 0$
$\Rightarrow | a | = | b |$
$\sqrt{{(3)}^{2} + {(- 4)}^{2} + {(2)}^{2}} [∵ b = 3^i - 4^j + 2^k]$
$= \sqrt{29}$

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Similar questions

Let $a =^i + 4^j + 2^k, b = 3^i - 2^j + 7^k$ and $c = 2^i -^j + 4^k$ . Find a vector d which is perpendicular to both a and b and c.d = 15

Let a $\to a =^1 + 4^J + 2^k, \to b = 3^i - 2^j + 7^k a n d c = 2^i -^j + 4^k .$ find a vector $\to d$ which is perpendicular to both $\to a$ and $\to b$ and $\to c . \to d = 27.$

Q. Let

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Q. Let

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Find a unit vector perpendicular to each of the vectors a + b and a - b, where $a = 3^i + 2^j + 2^k$ and $b =^i + 2^j - 2^k$

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If a+b and a−b are perpendicular and b=3^i−4^j+2^k, then |a| is equal to

The correct option is C √29Given,(a+b) and (a−b) are perpendicular∴ (a+b).(a−b)=0⇒ a2−b2=0⇒|a|=|b|√(3)2+(−4)2+(2)2[∵b=3^i−4^j+2^k]=√29

If $a + b$ and $a - b$ are perpendicular and $b = 3^i - 4^j + 2^k$ , then $| a |$ is equal to

The correct option is C $\sqrt{29}$
Given,
$(a + b)$ and $(a - b)$ are perpendicular
$∴$ $(a + b) . (a - b) = 0$
$\Rightarrow$ $a^{2} - b^{2} = 0$
$\Rightarrow | a | = | b |$
$\sqrt{{(3)}^{2} + {(- 4)}^{2} + {(2)}^{2}} [∵ b = 3^i - 4^j + 2^k]$
$= \sqrt{29}$