The unit vector in ZOX plane- making angles 45- and 60- respectively with -2 -2 -k- and -k- isA- 1-2-1-2-B- 1-2-1-2k-C- 1-2-1-2-D- 1-2-1-2k-

The correct option is B 1√(2)î 1√(2)k̂Vector in ZOX plane is aî+ck̂ nbsp; ∴(2î+ 2ĵ k̂). (aî+ck̂)3 √(a^2+c^2) = 1√(2) and (ĵ k̂). (aî+ck̂)√(2)√(a^2+c^2) = 1 ...

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Byju's Answer

Standard XII

Mathematics

Perpendicular Distance of a Point from a Plane

The unit vect...

Question

The unit vector in $Z O X$ plane, making angles $45^{\circ} and 60^{\circ}$ respectively with $\to α = 2^i + 2^j -^k and \to β =^j -^k$ is

\frac{1}{\sqrt{2}}^i + \frac{1}{\sqrt{2}}^j

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\frac{1}{\sqrt{2}}^i - \frac{1}{\sqrt{2}}^k

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\frac{1}{\sqrt{2}}^i - \frac{1}{\sqrt{2}}^j

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\frac{1}{\sqrt{2}}^i + \frac{1}{\sqrt{2}}^k

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Solution

The correct option is B $\frac{1}{\sqrt{2}}^i - \frac{1}{\sqrt{2}}^k$
Vector in $Z O X$ plane is $a^i + c^k$
$∴ \frac{(2^i + 2^j -^k) . (a^i + c^k)}{3 \sqrt{a^{2} + c^{2}}} = \frac{1}{\sqrt{2}} and \frac{(^j -^k) . (a^i + c^k)}{\sqrt{2} \sqrt{a^{2} + c^{2}}} = \frac{1}{2}$
Solve to get $a = \frac{1}{\sqrt{2}}, c = \frac{- 1}{\sqrt{2}}$
(or)
checking the options
$\frac{^i}{\sqrt{2}} - \frac{^k}{\sqrt{2}} .$

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Similar questions

Q. The unit vector in ZOX plane and making angle

45^{\circ}

and

60^{\circ}

respectively with

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

and

\to b = 0^i +^j -^k

Q. A unit vector perpendicular to the plane determined by the points P(1,-1,2), Q(2,0,-1) and R(0,2,1) is

Q. Find the unit vector in the direction of the resultant of vectors

^i + 2^j + 3^k, -^i + 2^j +^k

and

3^i +^j

Q. If

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

, and

\to c

is unit vector perpendicular to the vector

\to a

and coplanar with

\to a

and

\to b

then a unit vector

\to d

perpendicular to both

\to a

and

\to c

, is

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The unit vector in ZOX plane, making angles 45∘ and 60∘ respectively with→α=2^i+2^j−^k and →β=^j−^k is

The correct option is B 1√2^i−1√2^kVector in ZOX plane is a^i+c^k ∴(2^i+2^j−^k).(a^i+c^k)3√a2+c2=1√2 and (^j−^k).(a^i+c^k)√2√a2+c2=12 Solve to get a=1√2,c=−1√2 (or) checking the options ^i√2−^k√2.

The unit vector in $Z O X$ plane, making angles $45^{\circ} and 60^{\circ}$ respectively with $\to α = 2^i + 2^j -^k and \to β =^j -^k$ is