Let A- be vector parallel to line of intersection of planes P1 and P2 through origin- P1 is parallel to the vectors 2-3k- and 4-3k- and P2 is parallel to -k- and 3i -3- then the angle between vectors A and 2-2k- is

The correct options are C 3π/4 D π/4 Vector AB is parallel to [(2ĵ+̂ 3k̂ #160;)×(4ĵ ̂ 3k̂]×[(ĵ k̂)×(3î+3ĵ)]=54(ĵ k̂) #160;Let θ is th ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

Let A⃗ be v...

Question

Let $\to A$ be vector parallel to line of intersection of planes $P_{1}$ and $P_{2}$ through origin. $P_{1}$ is parallel to the vectors $2^j + 3^k$ and $4^j - 3^k$ and $P_{2}$ is parallel to $^j -^k$ and $3 i + 3^j$ , then the angle between vectors $¯ ¯¯ ¯ A$ and $2^i +^j - 2^k$ is

\frac{π}{2}

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\frac{π}{4}

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\frac{π}{6}

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\frac{3 π}{4}

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Solution

The correct options are
C $\frac{3 π}{4}$
D $\frac{π}{4}$
Vector AB is parallel to $[(2^j + 3^k) \times (4^j - 3^k] \times [(^j -^k) \times (3^i + 3^j)] = 54 (^j -^k)$
Let $θ$ is the angle between the vector, then $cos θ = \pm (\frac{54 + 108}{3.54 \sqrt{2}}) = \pm \frac{1}{\sqrt{2}}$
Hence $θ = \frac{π}{4}, \frac{3 π}{4}$ .

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Similar questions

Q. Let

\to A

be vector parallel to line of intersection of planes

P_{1}

and

P_{2}

through origin.

P_{1}

is parallel to the vector

2^j + 3^k

and

4^j - 3^k

and

P_{2}

is parallel to

^j -^k

and

3^i + 3^j

, then the angle between vector

\to A

and

2^i +^j - 2^k

Q. Let

\to A

be vector parallel to line of intersection of planes

P_{1}

and

P_{2}

, Plane

P_{1}

is parallel to the vectors

2^j + 3^k

and

4^j - 3^k

and that

P_{2}

is parallel to

^j -^k

and

3^i + 3^j

then the angle between vector

\to A

and a given vector

2^i +^j - 2^k

Q. Let

\to A

be vector parallel to line of intersection of planes

P_{1}

and

P_{2}

through origin.

P_{1}

is parallel to the vectors

2^j + 3^k

and

4^j - 3^k

and

P_{2}

is parallel to

^j -^k

and

3^i + 3^j,

then the angle between vector

\to A

and

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

Q. Let

\to A

be vector parallel to the line of intersection of planes

p_{1}

and

p_{2}

through the origin.

p_{1}

is parallel to the vectors

\to a = 2^j + 3^k

and

\to b = 4^j - 3^k

and

p_{2}

is parallel to the vectors

\to c =^j -^k

and

\to d = 3^i + 3^j

. The angle between

\to A

and

2^i +^j - 2^k

is:

Q. Assertion :

Consider planes

P_{1} : (\to r -^i) . (^i -^j -^k) = 0

and

P_{2} : (\to r - (2^i -^j -^k)) . (^i - 2^k) \times (2^i -^j - 3^k) = 0

and line

L : \to r = 5^i + λ (^i -^j -^k)

P_{1}

and

P_{2}

are parallel planes Reason:

L

is parallel to both

P_{1}

and

P_{2}

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Let →A be vector parallel to line of intersection of planes P1 and P2 through origin. P1 is parallel to the vectors 2^j+3^k and 4^j−3^k and P2 is parallel to ^j−^k and 3i+3^j, then the angle between vectors ¯¯¯¯A and 2^i+^j−2^k is

The correct options are C 3π4 D π4Vector AB is parallel to [(2^j+3^k)×(4^j−3^k]×[(^j−^k)×(3^i+3^j)]=54(^j−^k) Let θ is the angle between the vector, then cosθ=±(54+1083.54√2)=±1√2 Hence θ=π4, 3π4 .

Let $\to A$ be vector parallel to line of intersection of planes $P_{1}$ and $P_{2}$ through origin. $P_{1}$ is parallel to the vectors $2^j + 3^k$ and $4^j - 3^k$ and $P_{2}$ is parallel to $^j -^k$ and $3 i + 3^j$ , then the angle between vectors $¯ ¯¯ ¯ A$ and $2^i +^j - 2^k$ is