Let a -3 -2 -2 k- and b -2 -2 k- be two vectors- If a vector perpendicular to both the vectors a - b and a - b has themagnitude 12 then one such vector is -A- 42 -2 -k-B- 42 -2 -k-C- 42 -2 -k-D- 4-2 -2 -k-

A=3î +2ĵ+2k̂ b=î +2ĵ 2k̂ a+b=4î+4ĵ a b=2î+4k̂ As nbsp;a vector rperpendicular to both the vectors a+ nbsp; b and nbsp;a nbsp; b has the magnitude 12 r= ...

You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

Let a =3 î+2 ...

Question

Let $\to a = 3^i + 2^j + 2^k$ and $\to b =^i + 2^j - 2^k$ be two vectors. If a vector perpendicular to both the vectors $\to a + \to b$ and $\to a - \to b$ has the magnitude $12$ then one such vector is :

4 (2^i + 2^j +^k)

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

4 (2^i + 2^j -^k)

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

4 (2^i - 2^j -^k)

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

4 (- 2^i - 2^j +^k)

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

Open in App

Solution

The correct option is C $4 (2^i - 2^j -^k)$
$\to a = 3^i + 2^j + 2^k$
$\to b =^i + 2^j - 2^k$
$\to a + \to b = 4^i + 4^j$
$\to a - \to b = 2^i + 4^k$
As a vector $\to r$ perpendicular to both the vectors $\to a + \to b$ and $\to a - \to b$ has the magnitude $12$
$\to r = 12 \cdot^n$
$^n = \frac{(\to a + \to b) \times (\to a - \to b)}{∣ ∣ ∣ (\to a + \to b) \times (\to a - \to b) ∣ ∣ ∣}$

$^n = \frac{8 [2^i - 2^j -^k]}{8 \cdot \sqrt{4 + 4 + 1}} = \frac{2^i - 2^j -^k}{3}$

$∴ \to r = \frac{12}{3} (2^i - 2^j -^k) = 4 (2^i - 2^j -^k)$

Suggest Corrections

Similar questions

Q. Let

\to a = 3^i + 2^j + 2^k

and

\to b =^i + 2^j - 2^k

be two vectors. If a vector perpendicular to both the vectors

\to a + \to b

and

\to a - \to b

has the magnitude

12

then one such vector is :

Q. Component of vector

\to A = 3^i + 2^j +^k

perpendicular to vector

\to B =^i - 2^j

Q. The unit vector which, is perpendicular to the vectors

\to A =^i - 2^j +^k

and

\to B = 3^i - 2^j -^k

Q. Let

\to a = 3^i + 2^j + 2^k, b =^i + 2^j - 2^k

. Then a unit vector perpendicular to both

\to a - \to b

and

\to a + \to b

is :

Find a unit vector perpendicular to each of the vectors a + b and a - b, where $a = 3^i + 2^j + 2^k$ and $b =^i + 2^j - 2^k$

Join BYJU'S Learning Program

Let →a=3^i+2^j+2^k and →b=^i+2^j−2^k be two vectors. If a vector perpendicular to both the vectors →a+→b and →a−→b has the magnitude 12 then one such vector is :

Let $\to a = 3^i + 2^j + 2^k$ and $\to b =^i + 2^j - 2^k$ be two vectors. If a vector perpendicular to both the vectors $\to a + \to b$ and $\to a - \to b$ has the magnitude $12$ then one such vector is :