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•  a ⃗-[(a ⃗∙n ⃗)/(b ⃗∙n ⃗ )] b ⃗
•  a ⃗-[(a ⃗∙n ⃗)/(b ⃗∙n ⃗ )] b ⃗
•  None of these
• Solution
The straight line r ⃗=a ⃗+Î» b ⃗ meets the plane r ⃗∙n ⃗=0 in P for which Î» is given by (a ⃗+Î» b ⃗ )∙n ⃗=0⇒Î»=-(a ⃗∙n ⃗)/(b ⃗∙n ⃗ ) Thus, the position vector of P is r ⃗=a ⃗((a ⃗∙n ⃗)/(b ⃗∙n ⃗ )) b ⃗ [Putting the value of Î» in r ⃗=a ⃗+Î»b ⃗ ]

Q8.Cosine of the angle between two diagonals of cube is equal to
•  2/√6
•  1/3
•  1/2
•  None of these
Solution
Let OA,OB,OC be the sides of a cube such that OA=OB=OC=a ∴ Direction ratios of OE are (a-0,a-0)ie (a,a,a) ∴Direction cosines of AF are (1/√3,1/√3,1/√3) Similarly, direction of AF are (-1/√3,1/√3,1/√3). ∴ Angle between OE and AF is cos^(-1)⁡〖[-1/√3∙1/√3+1/√3∙1/√3+1/√3∙1/√3] cos^(-1)⁡(1/3) 〗

Q9.The line segment adjoining the points A, B makes projection 1, 4, 3 on x, y, z-axes respectively. Then, the direction cosines of AB are
•  1, 4, 3
•  1/√26,-4/√26,3/√26
•  -1/√26,4/√26,3/√26
•  1/√26,4/√26,3/√26
Solution
DC^' s of AB=1/√(1^2+4^2+3^2 ),4/√(1^2+4^2+3^2 ),3/√(1^2+4^2+3^2 ) =1/√26,4/√26,3/√26

Q10.  A variable plane moves so that sum of the reciprocals of its intercepts on the coordinate axes is 1/2 Then, the plane passes through
•  (1/2,1/2,-1/2)
•  (2, 2, 2)
•  (-1,1,1)
• (0, 0, 0)
Solution
Let x/a+y/b+z/c=1 ….(i) Then,1/a+1/b+1/c=1/2 …(ii) On comparing Eqs. (i) and (ii), we get x=2,y=2,z=2

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