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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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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 shortest distance betwen L_1 and L_2 is (A) 0 (B) 17/sqrt(3) (C) 41/(5(3) (D) 17/sqrt(75)

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

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

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 sides of a parallelogram are 2hati+4hat-5hatk and hati+2hatj+3hatk . The unit vector parallel to one of the diagonal is (A) 1/sqrt(69)(hati+2hatj-8hatk) (B) 1/sqrt(69)(-hati+2hatj+8hatk) (C) 1/sqrt(69)(-hati-2hatj-8hatk) (D) 1/sqrt(69)(hati+2hatj+8hatk)

The foot of the perpendicular from the point (1,2,3) on the line vecr=(6hati+7hatj+7hatk)+lamda(3hati+2hatj-2hatk) has the coordinates

The shortest distance between the lines r = ( - hati - hatj - hatk ) + lamda ( 7 hati - 6 hatj + hatk ) and r = ( 3 hati + 5 hatj + 7 hatk ) + mu ( hati - 2 hatj + hatk )

Two vectors vecalpha=3hati+4hatj and vecbeta5hati+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)

If p_(1) and p_(2) are the lengths of perpendiculars from the points hati - hatj + 3hatk and 3hati + 4hatj + 3hatk to the plane barr *(5hati + 2hatj - 7hatk) + 8 = 0 , then