MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Applications of Dot Product

If a and ...

Question

If $\to a$ and $\to b$ are unit vectors such that $| \to a + \to b | = 1$ , then find the value of $| \to a - \to b |$

Open in App

Solution

Consider the problem

$\begin{matrix} | \to a | = ∣ ∣ \to b ∣ ∣ = 1 ∣ ∣ \to a + \to b ∣ ∣ = 1 \Rightarrow {∣ ∣ \to a + \to b ∣ ∣}^{2} = 1 \Rightarrow (\to a + \to b) . (\to a + \to b) = 1 (\to a . \to a = {| \to a |}^{2}) \Rightarrow \to a . \to a + \to a . \to b + \to b . \to a + \to b . \to b = 1 \Rightarrow {| \to a |}^{2} + 2 \to a . \to b + {∣ ∣ \to b ∣ ∣}^{2} = 1 (∵ \to a . \to b = \to b . \to a) \Rightarrow 1 + 2 \to a . \to b + 1 = 1 \Rightarrow 2 \to a . \to b = - 1 \Rightarrow \to a . \to b = - \frac{1}{2} . . . (1) \end{matrix}$

Now

$\begin{matrix} {∣ ∣ \to a - \to b ∣ ∣}^{2} = (\to a - \to b) . (\to a - \to b) = \to a . \to a - \to a . \to b - \to b . \to a + \to b . \to b = {| \to a |}^{2} - 2 \to a . \to b + {∣ ∣ \to b ∣ ∣}^{2} = 1 - 2 \times \frac{- 1}{2} + 1 (f r o m (1)) = 1 + 1 + 1 = 3 \end{matrix}$

$\Rightarrow ∣ ∣ \to a - \to b ∣ ∣ = \sqrt{3}$

Suggest Corrections

thumbs-up

0

Similar questions

¯ ¯ ¯ a

¯ ¯ b

are unit vectors such that

| ¯ ¯ ¯ a \times ¯ ¯ b | = ¯ ¯ ¯ a . ¯ ¯ b

| a - b |^{2} =

If a, b, c are unit vectors such that a + b + c = 0, then find the value of a.b + b.c + c.a

\hat{a}, \hat{b}

are unit vectors such that

\hat{a} + \hat{b}

is a unit vector, write the value of

|\hat{a} - \hat{b}| .

Q. If two vectors

\vec{a} and \vec{b}

|\vec{a}| = 2, |\vec{b}| = 1 and \vec{a} \cdot \vec{b} = 1,

then find the value of

(3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b}) .

\vec{a}

\vec{b}

are two unit vectors such that

\vec{a} + \vec{b}

is also a unit vector, then find the angle between

\vec{a}

\vec{b}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Dot Product

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Applications of Dot Product

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon