Dot Product: JEE Questions & Solutions

Let AB = 2 i + 4 j - 5 k and AD = i + 2 j + k, R. Let the projection of the vector v = i + j + k on the diagonal AC of the parallelogram…

Let a vector a= 2 i- j+ k, 0, make an obtuse angle with the vector b=- ^2 i+4 2 j+4 2 k and an angle, 6< < 2, with the positive z-axis. If…

Let a=2 i- j- k, b= i+3 j- k and c=2 i+ j+3 k. Let v be the vector in the plane of a and b, such that the length of its projection on the…

For three unit vectors a, b, c satisfying | a- b|^2 + | b- c|^2 + | c- a|^2 = 9 and |2 a + k b + k c| = 3, the positive value of k is:

Let a and b be two unit vectors such that the angle between them is 3. If a + 2 b and 3 a - b are perpendicular to each other, then the…

If a is a non-zero vector such that its projections on the vectors 2 i - j + 2 k, i + 2 j - 2 k, and k are equal, then a unit vector along…

Consider two vectors u = 3 i - j and v = 2 i + j - k, 0. The angle between them is given by ^-1 ( 52 7). Let v = v1 + v2, where v1 is…

Let the angle, 0 < < 2 between two unit vectors a and b be ^-1 ( 659). If the vector c = 3 a + 6 b + 9( a b), then the value of 9( c a) -…

Least positive integral value of, for which the angle between vectors i-2j+2k and i+2 j-2k is acute, is:

The least positive integral value of for which the angle between the vectors i - 2j + 2k and i + 2 j - 2k is acute is:

Let a unit vector u = x i + y j + z k make angles 2, 3, 2 3 with the vectors p1 = 1 2 i + 1 2 k, p2 = 1 2 j + 1 2 k, and p3 = 1 2 i + 1 2…

Let a unit vector u = x i + y j + z k make angles /2, /3, 2 /3 with the vectors p1 = (1/ 2)i + (1/ 2)k, p2 = (1/ 2)j + (1/ 2)k, and p3 =…

If 0, and is the angle between vectors a = i + j - 3 k and b = 3 i - j + 2 k, such that a + b and a - b are mutually perpendicular, then…

Let a = i + 2 j + 3 k, b = 2 i + 3 j - 5 k, and c = 3 i - j + k be three vectors. Let r be a unit vector along b + c. If r a = 3, then 3 is…

Vectors a = a i + b j + k and b = 2 i - 3 j + 4 k are perpendicular to each other when 3a + 2b = 7. The ratio of a to b is x/2. The value…

If two vectors P = i + 2 j + m k and Q = 4 i - 2 j + k are perpendicular to each other, then the value of m will be:

Let = 4 i + 3 j + 5 k and = i + 2 j - 4 k. Let 1 be parallel to and 2 be perpendicular to. If = 1 + 2, then the value of 5 2 ( i + j + k)…

If the vectors a = i + j + 4 k, b = -2 i + 4 j - 2 k, and c = 2 i + 3 j + k are coplanar, and the projection of a on vector b is 54 units,…

Let a and b be two vectors. Let | a| = 1, | b| = 4 and a b = 2. If c = (2 a b) - 3 b, then the value of b c is

Let a = 2 i + j + k, and b and c be two nonzero vectors such that | a + b + c | = | a + b - c | and b c = 0. Consider the following two…

Let a = 5 i - j - 3 k and b = i + 3 j + 5 k be two vectors. Then which one of the following statements is TRUE?