Given - A-1- - 2- A-2- - 3- and - A-1 - A-2- - 3- Find the value of A-1 - 2A-2-3A-1 - 4A-2-

The correct option is A 64 The value of, #160; #160; #160; (A_1 #160; + 2A_2 ).(3A_1 #160; 4A_2 ) ? #160; =3A _1^2 4A _1A _2 + ...

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Standard XII

Mathematics

Applications of Dot Product

Given | A⃗1...

Question

Given $∣ ∣ {\to A}_{1} ∣ ∣ = 2, ∣ ∣ {\to A}_{2} ∣ ∣ = \to 3$ and $∣ ∣ {\to A}_{1} + {\to A}_{2} ∣ ∣ = 3$ . Find the value of $({\to A}_{1} + 2 {\to A}_{2}) . (3 {\to A}_{1} - 4 {\to A}_{2})$ .

- 64

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60

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Solution

The correct option is A $- 64$
The value of,
$(- \to A_{1} + 2 - \to A_{2}) . (3 - \to A_{1} - 4 - \to A_{2}) ?$
$= 3 {\to A}_{1}^{2} - 4 {\to A}_{1} {\to A}_{2} + 6 {\to A}_{1} {\to A}_{2} - 8 {\to A}_{2}^{2}$
$= 3 {\to A}_{1}^{2} + 2 {\to A}_{1} {\to A}_{2} - 8 {\to A}_{2}^{2}$ , Where as $∴ {\to A}_{1} {\to A}_{2} = - 2$
$= 3 {| 2 |}^{2} + 2 (- 2) - 8 {| 3 |}^{2}$
= 12-4-72
= 12-76 = -64
So that the correct Ans. is option A
Hence,
${(∣ ∣ {\to A}_{1} + {\to A}_{2} ∣ ∣)}^{2} = 3^{2}$
then,
${∣ ∣ ∣ {\to A}_{1} ∣ ∣ ∣}^{2} + {∣ ∣ ∣ {\to A}_{2} ∣ ∣ ∣}^{2} + 2 {\to A}_{1} {\to A}_{2} = 9$
= $4 + 9 + 2 {\to A}_{1} {\to A}_{2} = 9,$
= $13 + 2 {\to A}_{1} {\to A}_{2} = 9$
= $2 {\to A}_{1} {\to A}_{2} = - 4$
$∴ {\to A}_{1} {\to A}_{2} = - 2$

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Given ∣∣→A1∣∣=2,∣∣→A2∣∣=→3 and ∣∣→A1+→A2∣∣=3. Find the value of (→A1+2→A2).(3→A1−4→A2).

Given $∣ ∣ {\to A}_{1} ∣ ∣ = 2, ∣ ∣ {\to A}_{2} ∣ ∣ = \to 3$ and $∣ ∣ {\to A}_{1} + {\to A}_{2} ∣ ∣ = 3$ . Find the value of $({\to A}_{1} + 2 {\to A}_{2}) . (3 {\to A}_{1} - 4 {\to A}_{2})$ .