Page 73 - Engineering Mathematics Workbook_Final

Vector Calculus

127. The value of  Fdr where (d) R R = d R

C
dt
=
+
F xyi + yzj zxk and C is the curve
[GATE-2005 ; (IN)]
+
=
2
3
+
r ti t j t k from t = to t = 1is ____ 131. The area of a triangle formed by the tips
0
28 27 of vectors a , b and c is
(a) (b)
27 28
1 ( ) ( )
−
−
29 (a) a b  a c
(c) (d)1 2
28
) (
)
1
−
−
128. Let p = 3i + 2 j k and q i = + 2j + 3k be (b) ( a b  a c
+
2
+
+
vectors in R .Suppose V = ai bj ck is a
3
1


=
unit vector such that v .p = 0 v .q The (c) 2 a b c
value of a b c = _____ 1
+ +

(d) ( a b  ) c
(a) 6 (b) 3 2
(c) 1 (d) 0 [GATE-2007-ME]
129. If P, Q and R are three points having
coordinates (3, -2, -1), (1, 3, 4), (2, 1, -2) 132. If a and b are two arbitrary vectors
in XYZ space (o being the origin of the with magnitudes a and b, respectively,
2
coordinate system) then distance of point a b will be equal to

P from plane OQR is
(a) 3 (b) 7 2 2 ( ) 2

(a) a b − a b
(c) 5 (d) 9

−
(b) ab a b
[GATE-2003]

R
130. If a vector ( ) t has a constant (c) a b + 2 2 ( a b ) 2
magnitude than
+
(d) ab a b [GATE-2011-CE]
d R
(a) R  = 0
dt 133. If A (0, 4, 3), B (0, 0, 0) and C (3, 0, 4)
are three points defined in x, y, z
d R
(b) R  = 0 coordinate system, then which one of the
dt following vectors is perpendicular to

both the vectors AB and BC
d R
(c) R R = 0
dt

71