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The Earth and the Sun

To find angle...

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To find angle between a vector and x axis

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Q. Find the values of x for which the angle between the vectors

\to a = x^i - 3^j - 1^k

\to b = 2 x^i + x^j - 1^k

is acute and the angle between the vector b and y-axis is obtuse.

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

\to B =^i +^j

, then
(i) find the angle between

\to A

\to B

(ii) find the projection of resultant vector of

\to A

\to B

on x-axis.
(iii) find a vector which is, if added to

\to A

, gives a unit vector along y-axis.

θ

between the vector

¯ p =^i +^j +^k

and unit vector along x-axis is

θ

between the vector

¯ p =^i +^j +^k

and unit vector along x-axis is.

Q. The values of

x

for which the angle between the vectors

a = x i - 3 j - k

b = 2 x i + x j - k

is acute, and the angle between the vector

b

and the axis of ordinates is obtuse, are

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