CameraIcon

SearchIcon

MyQuestionIcon

1

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

Applications of Dot Product

Let a⃗, b⃗...

Question

Let $\to a$ , $\to b$ and $\to c$ be three vectors such that $| \to a | = 3 ∣ ∣ \to b ∣ ∣ = 4 | \to c | = 5$ and each one of them being perpendicular to the sum of the other two find $∣ ∣ \to a + \to b + \to c ∣ ∣$ .

Open in App

Solution

$\begin{matrix} | \to a | = 3, ∣ ∣ \to b ∣ ∣ = 4, | \to c | = 5 \to a \cdot (\to b + \to c) = 0 \to b \cdot (\to a + \to c) = 0 \to c \cdot (\to a + \to b) = 0 \to a \cdot \to b + \to a \cdot \to c = 0 \to b \cdot \to a + \to b \cdot \to c = 0 \to c \cdot \to a + \to c \cdot \to b = 0 \to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a = 0 {∣ ∣ \to a + \to b + \to c ∣ ∣}^{2} = {| a |}^{2} + {| b |}^{2} + {| c |}^{2} + 2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a) = 9 + 16 + 25 + 2 \times 0 = 50 ∣ ∣ \to a + \to b + \to c ∣ ∣ = 5 \sqrt{2} \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

\to a, \to b, \to c

be three vectors such that

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

| \to c | = 5

and each one of the perpendicular to the sum of the other two, find

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

\to a; \to b; \to c

are three vectors so that each one is perpendicular to the sum of the other two and also

| \to a | = 40; | \to b | = 20; | \to c | = 4

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

\to a, \to b

\to c

be three vectors such that

| \to a | = \sqrt{3}, | \to b | = 5, \to b . \to c = 10

and the angle between

\to b

\to c

\frac{π}{3} .

\to a

is perpendicular to vector

\to b \times \to c

| \to a \times (\to b \times \to c) |

\to a, \to b, \to c

be three units vectors such that

\to a \times (\to b \times \to c) = \frac{\to b + \to c}{\sqrt{2}}

and the angles between

\to a, \to c

\to a, \to b

α

β

respectively, then

\to a, \to b, \to c

be vectors of length

3, 4, 5

respectively. Let

\to a

be perpendicular to

\to b + \to c, \to b

\to c + \to a

\to c

\to a + \to b .

∣ ∣ \to a + \to b + \to c ∣ ∣

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