If a-6 -8 k- b -10 - 4 c - a - b and 2 d - a - b then which of the following statement is-are correct-A- - c - p d - c - p d - - p - RB- c is perpendicular to dC- c - d is perpendicular to c - dD- - a - b -5- c -5- d -

The correct options are A |c+pd|=|c pd| ∀ p∈ R B c is perpendicular to d C c+d is perpendicular to c d D |a|=|b| = √(5)|c|=√(5)|d| nbsp;c=4î+2k̂ d= 2î+4k̂ ...

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Byju's Answer

Standard XII

Mathematics

Combination of r Things from n Things When All Are Not Different

If a⃗=6 î+8 k...

Question

If $\to a = 6^i + 8^k, \to b = 10^i, 4 \to c = \to a + \to b$ and $2 \to d = \to a - \to b$ then which of the following statement is/are correct?

| \to c + p \to d | = | \to c - p \to d | \forall p \in R

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\to c

is perpendicular to

\to d

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\to c + \to d

is perpendicular to

\to c - \to d

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| \to a | = | \to b | = \sqrt{5} | \to c | = \sqrt{5} | \to d |

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Solution

The correct options are
A $| \to c + p \to d | = | \to c - p \to d | \forall p \in R$
B $\to c$ is perpendicular to $\to d$
C $\to c + \to d$ is perpendicular to $\to c - \to d$
D $| \to a | = | \to b | = \sqrt{5} | \to c | = \sqrt{5} | \to d |$
$\to c = 4^i + 2^k$
$\to d = - 2^i + 4^k$
$\to c \cdot \to d = (4^i + 2^k) \cdot (- 2^i + 4^k) = 0$

$| \to c + p \to d |^{2} = | \to c |^{2} + p^{2} | \to d |^{2} + 2 p \to c \cdot \to d \Rightarrow | \to c + p \to d | = \sqrt{| \to c |^{2} + p^{2} | \to d |^{2}}$
Similarly,
$| \to c - p \to d | = \sqrt{| \to c |^{2} + p^{2} | \to d |^{2}}$
So,
$| \to c + p \to d | = | \to c - p \to d |$

$(\to c + \to d) \cdot (\to c - \to d) = | \to c |^{2} - | \to d |^{2} = 0$

$| \to a | = 10$
$| \to b | = 10$
$| \to c | = \sqrt{20}$
$| \to d | = \sqrt{20}$
$\Rightarrow | \to a | = | \to b | = \sqrt{5} | \to c | = \sqrt{5} | \to d |$

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If →a=6^i+8^k, →b=10^i, 4→c=→a+→b and 2→d=→a− →b then which of the following statement is/are correct?

If $\to a = 6^i + 8^k, \to b = 10^i, 4 \to c = \to a + \to b$ and $2 \to d = \to a - \to b$ then which of the following statement is/are correct?