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A paragraph has been given. Based upon t...

A paragraph has been given. Based upon this paragraph, 3 multiple choice question have to be answered. Each question has 4 choices a,b,c and d out of which ONLYONE is correct. Consider the `L_1:(x+1)/3=(y+2)/1=(z+1)/2 and L_2:(x-2)/1=(y+2)/2=(z-3)/3` The unit vector perpendicular to both `L_1 and L_2` is (A) `(-hati+7hatk+7hatk)/sqrt(99)` (B) `(-hati-7hatk+5hatk)/(5sqrt(3))` (C) `(-hati+7hatk+7hatk)/(5sqrt(3))` (D) `(7hati-7hatk-7k)/sqrt(99)`

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Unit vectors equally inclined to the vectors hati , 1/3 ( -2hati +hatj +2hatk) = +- 4/sqrt3 ( 4hatj +3hatk) are

Vectors perpendicular to hati-hatj-hatk and in the plane of hati+hatj+hatk and -hati+hatj+hatk are (A) hati+hatk (B) 2hati+hatj+hatk (C) 3hati+2hatj+hatk (D) -4hati-2hatj-2hatk

The length of perpendicular from the origin to the line vecr=(4hati+2hatj+4hatk)+lamda(3hati+4hatj-5hatk) is (A) 2 (B) 2sqrt(3) (C) 6 (D) 7

A unit vector int eh plane of the vectors 2hati+hatj+hatk, hati-hatj+hatk and orthogonal to 5hati+2hatj-6hatk is (A) (6hati-5hatk)/sqrt(6) (B) (3hatj-hatk)/sqrt(10) (C) (hati-5hatj)/sqrt(29) (D) (2hati+hatj-2hatk)/3

The vector (s) equally inclined to the vectors hati-hatj+hatk and hati+hatj-hatk in the plane containing them is (are_ (A) (hati+hatj+hatk)/sqrt(3) (B) hati (C) hati+hatk (D) hati-hatk

Show that a unilt vector perpendicular to each to the vector 3hati+hatj+2hatk and 2hati-2hatj+4hatk is 1/sqrt(3)(hati-hatj-hatk) and the sine of the angle between them is 2/sqrt(7) .

The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk and is coplanar with the vectors 2hati+hatj+hatk and hati-hatj+hatk is (A) (2hati-6hatj+hatk)/sqrt(41) (B) (2hati-3hatj)/sqrt(3) (C) 3hatj-hatk)/sqrt(10) (D) (4hati+3hatj-3hatk)/sqrt(34)

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The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is (a) (2hati - 6hatj + hatk)/sqrt41 (b) (2hati-3hatj)/sqrt13 (c) (3 hatj -hatk)/sqrt10 (d) (4hati + 3hatj - 3hatk)/sqrt34

Two vectors vecalpha=3hati+4hatj and vecbeta=5hati+2hatj-14hatk have the same initial point then their angulr bisector having magnitude 7/3 be (A) 7/(3sqrt(6))(2hati+hatj-hatk) (B) 7/(3sqrt(3))(\hati+hatj-hatk) (C) 7/(3sqrt(3))(hati-hatj+hatk) (D) 7/(3sqrt(3))(hati-hatj-hatk)