If the vector b is collinear with a-2-2-1-4 and -b-10- then

A=(2√(2), 1,4) and |b|=10 Given vector b is collinear with a. b=ka ⇒ |b|=10 ⇒ nbsp; 10=√((2√(2)k)^2+( 1k)^2+(4k)^2) ⇒ 25k^2=100 ∴ k=±2 ⇒b=± 2a ...

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

Byju's Answer

Standard XII

Mathematics

Angle between Two Line Segments

If the vector...

Question

If the vector $\to b$ is collinear with $\to a = (2 \sqrt{2}, - 1, 4)$ and $| \to b | = 10,$ then

\to a = \pm \to b

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

\to a = \pm 2 \to b

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

\to b = \pm \to a

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

\to b = \pm 2 \to a

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

Open in App

Solution

The correct option is D $\to b = \pm 2 \to a$
$\to a = (2 \sqrt{2}, - 1, 4)$ and $| \to b | = 10$
Given vector $\to b$ is collinear with $\to a .$
$\to b = k \to a$
$\Rightarrow | \to b | = 10$
$\Rightarrow 10 = \sqrt{(2 \sqrt{2} k)^{2} + (- 1 k)^{2} + (4 k)^{2}}$
$\Rightarrow 25 k^{2} = 100$
$∴ k = \pm 2$
$\Rightarrow \to b = \pm 2 \to a$

Suggest Corrections

Similar questions

Q. Let

\to a, \to b

and

\to c

are three nonzero, non collinear vectors. If the vector

3 \to a + 7 \to b

is collinear with

\to c

and

3 \to b + 2 \to c

is collinear with

\to a

, then

∣ ∣ 9 \to a + 21 \to b + 14 \to c ∣ ∣

is equal to

Q. Let

\to a, \to b

and

\to c

be there non-zero vectors such that no two of these are collinear. If the vector

\to a + 2 \to b

is collinear with

\to c

and

\to b + 3 \to c

is collinear with

\to a

then

\to a + 2 \to b + 6 \to c

equals

Let $\to a, \to b$ and $\to c$ be three non -zero vectors such that they are mutually non collinear. If the vector $\to a + 2 \to b$ is collinear with $\to c$ and $\to b + 3 \to c$ is collinear with $\to a$ then $\to a + 2 \to b + 6 \to c$ equals

Q. Let

\to a, \to b, \to c

be three non zero vectors which are pairwise non-collinear. If

\to a + 3 \to b

is collinear and

\to b + 2 \to c

is collinear with

\to a

, then

\to a + 3 \to b + 6 \to c

Let $\to a, \to b$ and $\to c$ be three non -zero vectors such that no two of these are collinear. If the vector $\to a + 2 \to b$ is collinear with $\to c$ and $\to b + 3 \to c$ is collinear with $\to a$ $(λ$ being some non -zero scalar) then $\to a + 2 \to b + 6 \to c$ equals

Join BYJU'S Learning Program

Explore more

Angle between Two Line Segments

Standard XII Mathematics

Join BYJU'S Learning Program

If the vector →b is collinear with →a=(2√2,−1,4) and |→b|=10, then

The correct option is D →b=±2→a→a=(2√2,−1,4) and |→b|=10 Given vector →b is collinear with →a. →b=k→a ⇒|→b|=10 ⇒10=√(2√2k)2+(−1k)2+(4k)2 ⇒25k2=100 ∴k=±2 ⇒→b=±2→a

If the vector $\to b$ is collinear with $\to a = (2 \sqrt{2}, - 1, 4)$ and $| \to b | = 10,$ then