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How many non ...

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How many non zero value of x and y for which the unit vectors 9^(x) i + α j + β k and 45^(y) i + γ j + δ k makes equal angle with x axis

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\to a = x^i + y^j + z^k

2 \sqrt{3} units,

which makes equal angles with the vectors

\to b = y^i - 2 z^j + 3 x^k

\to c = 2 z^i + 3 x^j - y^k

and is perpendicular to

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

and makes an obtuse angle with

y -

\to α =^i + 2^j -^k, \to β = 2^i -^j + 3^k

\to γ = 2^i +^j + 6^k

be three vectors. If

\to α

\to β

are both perpendicular to the vector

\to δ

\to δ . \to γ = 10

, then what is the magnitude of

\to δ

?

Q. If a unit vector

\to u = x^i + y^j + z^k

which makes an angle of

45^{\circ}

with the vector

2^i + 2^j -^k

and an angle of

60^{\circ}

with the vector

^j -^k .

P (x, y, z)

\to A = \to i + \to j

\to i, \to j

are unit vectors along X and Y axes respectively makes an angle of ______ with X-axis.

Q. The Unit Vectors orthogonal to

-^i + 2^j + 2^k

and making equal angles with

x

y

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