Magnitudes of vectors a- b- c- are 3-4-5 respectively- If a- and b-c- b- and c-a- c- and a-b- are mutually perpendicular- then the magnitude of a-b-c- is-A- 4 -2- 3 -2- 5 -2D- 3 -3

The correct option is C 5√(2)a·(b+c)=0 ⇒a·b+a·c=0 Similarly, b·c+b·a=0 c·a+c·b =0 Adding these 2(a·b+b·c+c·a)=0 Now |a+b+c|^2=|a|^2+|b|^2+|c|^2+2(a·b+b·c+c ...

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

Byju's Answer

Standard XII

Physics

Comparing Vectors

Magnitudes of...

Question

Magnitudes of vectors $\to a, \to b, \to c$ are $3, 4, 5$ respectively. If $\to a$ and $\to b + \to c$ , $\to b$ and $\to c + \to a$ , $\to c$ and $\to a + \to b$ are mutually perpendicular, then the magnitude of $\to a + \to b + \to c$ is,

4 \sqrt{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 \sqrt{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 \sqrt{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 \sqrt{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $5 \sqrt{2}$
$\to a \cdot (\to b + \to c) = 0 \Rightarrow \to a \cdot \to b + \to a \cdot \to c = 0$

Similarly, $\to b \cdot \to c + \to b \cdot \to a = 0$

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

Adding these $2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a) = 0$

Now $| \to a + \to b + \to c |^{2} = | \to a |^{2} + | \to b |^{2} + | \to c |^{2} + 2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a)$

$= 9 + 16 + 25 = 50$

$| \to a + \to b + \to c | = 5 \sqrt{2}$

Suggest Corrections

Similar questions

Q. Let

\to A = \to b \times \to c, \to B = \to c \times \to a, \to C = \to a \times \to b

, then the vectors

\to A \times (\to B \times \to C)

\to B \times (\to C \times \to A)

, and

\to C \times (\to A \times \to B)

are

Q. If

\to a, \to b, \to c

are three mutually perpendicular vectors of equal magnitude, prove that

(\to a + \to b + \to c)

is equally inclined with vectors

\to a, \to b

and

\to c

Q. If

\to a, \to b, \to c

are unit vectors such that

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

and

(\to a, \to b) = \frac{π}{3}

, then

∣ ∣ \to a \times \to b ∣ ∣ + ∣ ∣ \to b \times \to c ∣ ∣ + | \to c \times \to a | =

\to a, \to b, \to c

are mutually perpendicular vectors of equal magnitude then angle between

\to a + \to b + \to c

and

\to a

Q. If

\to a, \to b

and

\to c

are perpendicular to

\to b + \to c, \to c + \to a

and

\to a + \to b

respectively and if

| \to a + \to b | = 6, | \to b + \to c | = 8

and

| \to c + \to a | = 10

, then

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

is equal to

Join BYJU'S Learning Program

Magnitudes of vectors →a,→b,→c are 3,4,5 respectively. If →a and →b+→c, →b and →c+→a, →c and →a+→b are mutually perpendicular, then the magnitude of →a+→b+→c is,

Magnitudes of vectors $\to a, \to b, \to c$ are $3, 4, 5$ respectively. If $\to a$ and $\to b + \to c$ , $\to b$ and $\to c + \to a$ , $\to c$ and $\to a + \to b$ are mutually perpendicular, then the magnitude of $\to a + \to b + \to c$ is,