Given: a = <3, -2, 1>, b = <-5, 3, -3>. (01) The unit vector in the opposite direction of 3a - 2

01) The unit vector in the opposite direction of 3#26 is (A) <-2,-13,2837>.

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Given: a = <3, -2, 1>, b = <-5, 3, -3>. (01) The unit vector in the opposite direction of 3a - 2b is (A) <-2/3, -1/3, 2/3>; (B) <-19, 12, 9>; (C) <-4/5, 3/5, 0>; (D) <19, 0, 9>; (E) None of these. (02) If |a| = 4, |b| = 3 and the angle between a and b is ?/3, then a · b = (A) 3; (B) -6; (C) 6; (D) -3; (E) None of these. (03) What is the value of x such that the angle between <2, 1, -1> and <1, x, 0> is 30°? (A) -1; (B) 2; (C) -1/5; (D) 1/7; (E) None of these. (04) The scalar projection of b = <2, 3, -3> onto a = <2, -2, 1> is (A) -5/3; (B) -7/3; (C) -6/3; (D) 5/3; (E) None of these. (05) The vector projection of b = i - j + k onto a = 3j - 4k is (A) -21/25j + 28/25k; (B) -21/5i - 28/5j; (C) -3/25j + -4/25k; (D) -21/25i - 28/25k; (E) None of these. (06) A normal vector to the plane containing P(0, 0, -3), Q(4, 2, 0) and R(3, 3, 1) is (A) <3, 3, 4> · <4, 2, 3>; (B) <4, 2, 3> · <1, 0, 0>; (C) <3, 3, 4> x <4, 2, 3>; (D) <3, 3, 4> x <0, 1, 0>; (E) None of these. (07) A parametric equation of the line passing through (2, -3, 4) and parallel to <-1, 2, 5> is (A) x = -2+t, y = 3-2t, z = -4-5t; (B) x = -1+2t, y = 2-3t, z = 5+4t; (C) -(x-2) = (y+3)/2 = (z-4)/5; (D) x = 2-t, y = -3+2t, z = 4-5t; (E) None of these.. (08) A symmetric equation of the line passing through (2, 1, 0) and perpendicular to both i + 2j and -j + k is (A) (x-2) = (y+4) = (z-2); (B) (x-2)/2 = -(y-1) = -z; (C) (x+2) = -(y-4) = (z-2)/2; (D) (x-2) = (y+4) = (z-2)/2; (E) None of these. (09) A symmetric equation of the line passing through (2, -1, 5) and perpendicular to the plane -3x + 2y + z = 7 is (A) (x+1)/2 = (y-1) =(z+6)/3; (B) (x+1) = (y-1)/3 = (z+6); (C) -(x-2)/3 = (y+1)/2 = (z-5); (D) (x+2) = (y-1)/3 = (z+5); (E) None of these. (10) An equation of the plane through (1,-1,1) and parallel to the plane -3x+2y - z = 5 is (A) 3x - y - 3z = 8; (B) 2x + 3y - z = 5; (C) 3x - y -2z = 7; (D) -3x + 2y - z = - 6; (E) None of these. (11) An equation of the plane through (-2, 1, -5) and perpendicular to the line x = 2- 4t, y = 1+3t, z = 3 - t is (A) -4x + 3y - z = 16; (B) 4x - 2y + z = 16; (C) 4x - 3y + 2z = 7; (D) 3x - y + 4z = 10; (E) None of these.

          Given: a = <3, -2, 1>, b = <-5, 3, -3>. (01) The unit vector in the opposite direction of 3a - 2b is (A) <-2/3, -1/3, 2/3>; (B) <-19, 12, 9>; (C) <-4/5, 3/5, 0>; (D) <19, 0, 9>; (E) None of these. (02) If |a| = 4, |b| = 3 and the angle between a and b is ?/3, then a · b = (A) 3; (B) -6; (C) 6; (D) -3; (E) None of these. (03) What is the value of x such that the angle between <2, 1, -1> and <1, x, 0> is 30°? (A) -1; (B) 2; (C) -1/5; (D) 1/7; (E) None of these. (04) The scalar projection of b = <2, 3, -3> onto a = <2, -2, 1> is (A) -5/3; (B) -7/3; (C) -6/3; (D) 5/3; (E) None of these. (05) The vector projection of b = i - j + k onto a = 3j - 4k is (A) -21/25j + 28/25k; (B) -21/5i - 28/5j; (C) -3/25j + -4/25k; (D) -21/25i - 28/25k; (E) None of these. (06) A normal vector to the plane containing P(0, 0, -3), Q(4, 2, 0) and R(3, 3, 1) is (A) <3, 3, 4> · <4, 2, 3>; (B) <4, 2, 3> · <1, 0, 0>; (C) <3, 3, 4> x <4, 2, 3>; (D) <3, 3, 4> x <0, 1, 0>; (E) None of these. (07) A parametric equation of the line passing through (2, -3, 4) and parallel to <-1, 2, 5> is (A) x = -2+t, y = 3-2t, z = -4-5t; (B) x = -1+2t, y = 2-3t, z = 5+4t; (C) -(x-2) = (y+3)/2 = (z-4)/5; (D) x = 2-t, y = -3+2t, z = 4-5t; (E) None of these.. (08) A symmetric equation of the line passing through (2, 1, 0) and perpendicular to both i + 2j and -j + k is (A) (x-2) = (y+4) = (z-2); (B) (x-2)/2 = -(y-1) = -z; (C) (x+2) = -(y-4) = (z-2)/2; (D) (x-2) = (y+4) = (z-2)/2; (E) None of these. (09) A symmetric equation of the line passing through (2, -1, 5) and perpendicular to the plane -3x + 2y + z = 7 is (A) (x+1)/2 = (y-1) =(z+6)/3; (B) (x+1) = (y-1)/3 = (z+6); (C) -(x-2)/3 = (y+1)/2 = (z-5); (D) (x+2) = (y-1)/3 = (z+5); (E) None of these. (10) An equation of the plane through (1,-1,1) and parallel to the plane -3x+2y - z = 5 is (A) 3x - y - 3z = 8; (B) 2x + 3y - z = 5; (C) 3x - y -2z = 7; (D) -3x + 2y - z = - 6; (E) None of these. (11) An equation of the plane through (-2, 1, -5) and perpendicular to the line x = 2- 4t, y = 1+3t, z = 3 - t is (A) -4x + 3y - z = 16; (B) 4x - 2y + z = 16; (C) 4x - 3y + 2z = 7; (D) 3x - y + 4z = 10; (E) None of these.

Given: a = <3, -2, 1>, b = <-5, 3, -3>. (01) The unit vector in the opposite direction of 3a - 2b is (A) <-2/3, -1/3, 2/3>; (B) <-19, 12, 9>; (C) <-4/5, 3/5, 0>; (D) <19, 0, 9>; (E) None of these. (02) If |a| = 4, |b| = 3 and the angle between a and b is ?/3, then a · b = (A) 3; (B) -6; (C) 6; (D) -3; (E) None of these. (03) What is the value of x such that the angle between <2, 1, -1> and <1, x, 0> is 30°? (A) -1; (B) 2; (C) -1/5; (D) 1/7; (E) None of these. (04) The scalar projection of b = <2, 3, -3> onto a = <2, -2, 1> is (A) -5/3; (B) -7/3; (C) -6/3; (D) 5/3; (E) None of these. (05) The vector projection of b = i - j + k onto a = 3j - 4k is (A) -21/25j + 28/25k; (B) -21/5i - 28/5j; (C) -3/25j + -4/25k; (D) -21/25i - 28/25k; (E) None of these. (06) A normal vector to the plane containing P(0, 0, -3), Q(4, 2, 0) and R(3, 3, 1) is (A) <3, 3, 4> · <4, 2, 3>; (B) <4, 2, 3> · <1, 0, 0>; (C) <3, 3, 4> x <4, 2, 3>; (D) <3, 3, 4> x <0, 1, 0>; (E) None of these. (07) A parametric equation of the line passing through (2, -3, 4) and parallel to <-1, 2, 5> is (A) x = -2+t, y = 3-2t, z = -4-5t; (B) x = -1+2t, y = 2-3t, z = 5+4t; (C) -(x-2) = (y+3)/2 = (z-4)/5; (D) x = 2-t, y = -3+2t, z = 4-5t; (E) None of these.. (08) A symmetric equation of the line passing through (2, 1, 0) and perpendicular to both i + 2j and -j + k is (A) (x-2) = (y+4) = (z-2); (B) (x-2)/2 = -(y-1) = -z; (C) (x+2) = -(y-4) = (z-2)/2; (D) (x-2) = (y+4) = (z-2)/2; (E) None of these. (09) A symmetric equation of the line passing through (2, -1, 5) and perpendicular to the plane -3x + 2y + z = 7 is (A) (x+1)/2 = (y-1) =(z+6)/3; (B) (x+1) = (y-1)/3 = (z+6); (C) -(x-2)/3 = (y+1)/2 = (z-5); (D) (x+2) = (y-1)/3 = (z+5); (E) None of these. (10) An equation of the plane through (1,-1,1) and parallel to the plane -3x+2y - z = 5 is (A) 3x - y - 3z = 8; (B) 2x + 3y - z = 5; (C) 3x - y -2z = 7; (D) -3x + 2y - z = - 6; (E) None of these. (11) An equation of the plane through (-2, 1, -5) and perpendicular to the line x = 2- 4t, y = 1+3t, z = 3 - t is (A) -4x + 3y - z = 16; (B) 4x - 2y + z = 16; (C) 4x - 3y + 2z = 7; (D) 3x - y + 4z = 10; (E) None of these.

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