If a-b-2 c- a-b-4 c- and c-3 -4 - then what are a- and b- -

The correct option is D a b=2c.....................(1) a + b=4c....................(2) Solving equation (1) amp; (2) we get a=3c b=c ⇒a=3(3î+4ĵ) a=9î+12ĵ ...

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Byju's Answer

Standard XI

Mathematics

Insertion of HP's between 2 Numbers

If a⃗-b⃗=2 c⃗...

Question

If $\to a - \to b = 2 \to c$ , $\to a + \to b = 4 \to c$ and $\to c = 3^i + 4^j$ , then what are $\to a$ and $\to b$ ?

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Solution

The correct option is D

$\to a - \to b = 2 \to c$ .....................(1)

$\to a + \to b = 4 \to c$ ....................(2)

Solving equation (1) & (2) we get

$\to a = 3 \to c$

$\to b = \to c$

$\Rightarrow \to a = 3 (3^i + 4^j)$

$\to a = 9^i + 12^j$ (Scalar Multiplication)

$\to b = \to c = 3^i + 4^j$

Scalar Multiplication:-

When you multiply a vector by a constant also called as scalar here the direction of the new formed vector after multiplication will be same as the one on which scalar multiplication is done.

Only we multiply the constant to the magnitude of the vector.

Here $(3^i + 4^j)$ is multiplied by 3 and we get $9^i + 12^j$

Direction of $\to C = t a n^{- 1} (\frac{4}{3})$

Direction of $\to A = t a n^{- 1} (\frac{124}{93}) = t a n^{- 1} (\frac{4}{3})$

So direction of $\to C$ and are same

$| \to C | = \sqrt{3^{2} + 4^{2}} = 5 | \to A | = \sqrt{9^{2} + 12^{2}} = 15$

$3 \times | \to C | = | \to A |$

$3 \times 5 = 15$

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Nonzero vectors $\to a, \to b, \to c$ satisfy $\to a . \to b$ =0, $(\to b - \to a) . (\to b + \to c)$ = 0 and 2 $| \to b + \to c | = | \to b - \to a |$ .