Vector Algebra · Question 35

Let a = 2 i - j + 3 k, b = 3 i - 5 j + k and c be a vector such that a c = c b and ( a + c) ( b + c) = 168. Then the maximum value of | c|2 is :

1. 77
2. 154
3. 308
4. 462

Let a = i + j + k, b = 2 i + 2 j + k and d = a b. If c is a vector such that a c = | c|, | c - 2 a|2 = 8 and the angle between d and c is 4, then |10 - 3 b c| + | d c|2 is equal to .

If the components of a = i + j + k along and perpendicular to b = 3 i + j - k respectively, are 1611(3 i + j - k) and 111(-4 i - 5 j - 17 k), then 2 + 2 + 2 is equal to:

1. 16
2. 23
3. 26
4. 18

Let A, B, C be three points in xy-plane, whose position vectors are given by 3 i + j, i + 3 j and a i + (1 - a) j respectively with respect to the origin O. If the distance of the point C from the line bisecting the angle between the vectors OA and OB is 9 2, then the sum of all the possible values of a is:

1. 2
2. 0
3. 92
4. 1