The non-zero vectors a-b- and c- are related a- - 8b- and c- - - 7b- Then the angle between a- and c-

The correct option is D π →a=8→b , #160; →c= 7→b , #160; We are to find angle between →a amp; →b cosθ=→a·→c|→a |·|→c |= 5 ...

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Standard XII

Mathematics

Applications of Dot Product

The non-zero ...

Question

The non-zero vectors $\to a, \to b$ and $\to c$ are related $\to a = 8 \to b$ and $\to c = - 7 \to b$ . Then the angle between $\to a$ and $\to c$

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π / 4

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π

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Solution

The correct option is D $π$
$\to a = 8 \to b$ ,
$\to c = - 7 \to b$ ,
We are to find angle between $\to a$ & $\to b$
$cos θ = \frac{\to a \cdot \to c}{∣ \to a ∣ \cdot ∣ \to c ∣} = \frac{- 56 \to b \cdot \to b}{56 ∣ \to b ∣^{2}} = \frac{- 56 ∣ \to b ∣^{2}}{56 ∣ \to b ∣^{2}} = - 1$
$∴ θ = π$

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Similar questions

Q. If

\to a, \to b, \to c

are unit vectors and the angles between

\to a, \to b

and

\to b, \to c

and

\to c, \to a

are

\frac{π}{6}, \frac{π}{3}

and

\frac{π}{4}

respectively, then

| \to a + \to b + \to c |

Q. Vectors

\to a, \to b

and

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are such that

\to a + \to b + \to c = \to 0

and

| \to a | = 3, | \to b = 5

and

| \to c | = 7

. Find the angle between

\to a

and

\to b .

Q. The non-zero vectors

\to a, \to b

and

\to c

are related by

\to a = 8 \to b

and

\to c = - 7 \to b

, then the angle between

\to a

and

\to c

Q. If

\to a, \to b, \to c

are unit vectors such that

\to a \cdot \to b = 0 = \to a \cdot \to c

and the angle between

\to b

and

\to c

\frac{π}{3}

, then the value of

| \to a \times \to b - \to a \times \to c |

Q. If

(\to a, \to b) = \frac{π}{6}

\to c

is a perpendicular to

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and

\to b, | \to a | = 3, | \to b | = 4, | \to c | = 6

, then

| [\to a \to b \to c] | =

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The non-zero vectors →a,→b and →c are related →a=8→b and →c=−7→b. Then the angle between →a and →c

The correct option is D π→a=8→b, →c=−7→b, We are to find angle between →a & →bcosθ=→a⋅→c∣→a∣⋅∣→c∣=−56→b⋅→b56∣→b∣2=−56∣→b∣256∣→b∣2=−1∴θ=π

The non-zero vectors $\to a, \to b$ and $\to c$ are related $\to a = 8 \to b$ and $\to c = - 7 \to b$ . Then the angle between $\to a$ and $\to c$