IIT JEE 1983 Maths - True or False Q8

Geometry Level 3

True or False?

If x ⃗ ⋅ a ⃗ = 0 \vec x \cdot \vec a =0 , x ⃗ ⋅ b ⃗ = 0 \vec x \cdot \vec b =0 , x ⃗ ⋅ c ⃗ = 0 \vec x \cdot \vec c =0 for some non-zero vector x ⃗ \vec x , then the scalar triple product [ a ⃗ b ⃗ c ⃗ ] = 0 [\vec a \ \vec b \ \vec c ]=0 .

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .
True False

Shubhamkar Ayare by Shubhamkar Ayare , 22, India

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2 solutions

Nashita Rahman
Jan 31, 2017

Since the dot product of the three vectors with vector x is 0 , therefore the angle between them and vector x is 90° as cos90°=0.

Thus the vectors may be parallel to eachother or lie in the same plane. So the angle between each of the vectors is 0°. We know sin0°=0 and hence their scalar triple product is 0.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Prince Loomba
Jan 20, 2017

x is perpendicular to all, means they are coplanar or STP is 0.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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