A and c are unit vectors and - b -4- The angle between a and c is cos -11-4- If b -2 c - a- then - isA- 3 or -4B- 1-4 or 3-4C- -3 or 4 D- -1-4 or 3-4

The correct option is A 3 or 4 b 2c= λa⇒b=2c+λa ⇒ |b|^2=|2c+λa|^2 ⇒ 16=4 |c|^2+λ^2|a|^2+ 4 λ a.c ⇒ 16=4+λ^2+4 λ×1/4 ⇒λ^2+λ 12=0 ⇒λ=3, 4 ...

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Byju's Answer

Standard XII

Mathematics

Angle between Two Vectors

a and c are u...

Question

$\to a$ and $\to c$ are unit vectors and $| \to b | = 4.$ The angle between $\to a a n d \to c i s c o s^{- 1} (\frac{1}{4}) .$
If $\to b - 2 \to c = λ \to a$ , then $λ$ is

$3 o r - 4$

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$\frac{1}{4} o r \frac{3}{4}$

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$- 3 o r 4$

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$- \frac{1}{4} o r \frac{3}{4}$

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Solution

The correct option is A
$3 o r - 4$

$\to b - 2 \to c = λ \to a \Rightarrow \to b = 2 \to c + λ \to a \Rightarrow | \to b |^{2} = | 2 \to c + λ \to a |^{2} \Rightarrow 16 = 4 | \to c |^{2} + λ^{2} | \to a |^{2} + 4 λ \to a . \to c \Rightarrow 16 = 4 + λ^{2} + 4 λ \times \frac{1}{4} \Rightarrow λ^{2} + λ - 12 = 0 \Rightarrow λ = 3, - 4$

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→a and →c are unit vectors and |→b|=4. The angle between →a and →c is cos−1(14). If →b−2→c=λ→a, then λ is

The correct option is A 3 or −4 →b−2→c=λ→a⇒→b=2→c+λ→a⇒|→b|2=|2→c+λ→a|2⇒16=4|→c|2+λ2|→a|2+4λ →a.→c⇒16=4+λ2+4λ×14⇒λ2+λ−12=0⇒λ=3,−4

$\to a$ and $\to c$ are unit vectors and $| \to b | = 4.$ The angle between $\to a a n d \to c i s c o s^{- 1} (\frac{1}{4}) .$
If $\to b - 2 \to c = λ \to a$ , then $λ$ is