ExamHabit
Practise free

1995

JEE Main 1995 Mathematics question on Vector Algebra

Let u⃗\vec{u}, v⃗\vec{v} and w⃗\vec{w} be vectors such that u⃗+v⃗+w⃗=0⃗\vec{u} + \vec{v} + \vec{w} = \vec{0}. If ∣u⃗∣=3|\vec{u}| = 3, ∣v⃗∣=4|\vec{v}| = 4 and ∣w⃗∣=5|\vec{w}| = 5, then u⃗⋅v⃗+v⃗⋅w⃗+w⃗⋅u⃗\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u} is
  1. A.
    47
  2. B.
    -25
  3. C.
    0
  4. D.
    25
Show answer and solution

Correct option: B

Solution

Since u + v + w = 0, squaring both sides gives |u|² + |v|² + |w|² + 2(u·v + v·w + w·u) = 0. Substituting: 9 + 16 + 25 + 2(u·v + v·w + w·u) = 0, so 50 + 2(u·v + v·w + w·u) = 0, giving u·v + v·w + w·u = -25.

[1995]

Practise Vector Algebra the way it is asked

A timed set of real JEE Main Vector Algebra questions, graded as the exam grades. No sign-up.

Start a Vector Algebra test

More: all JEE Main Vector Algebra questions · JEE Main 1995 · Mathematics chapter list