Question

If the projection of a = i – 2j + 3k on b = 2i + λk is zero then find the value of λ

Answer 1

answer: a. b/|b|=0

a. b=0

(i-2j+3k).(2i+k)=0

2+3lamba=0

lambda=-2/3

Answer 2

λ = $\frac{-2}{3}$.

• Sometimes the inner product and the dot product are considered to be the same. The formal definitions of projection and rejection employ the inner product rather than the dot product whenever they don't coincide. The concepts of projecting a vector onto another and rejecting a vector from another can be applied to the concepts of projecting a vector onto a plane and rejecting a vector from a plane for a three-dimensional inner product space.
• A vector's orthogonal projection on a plane is the vector's projection on that plane. A vector is rejected from a plane when it is projected in an orthogonal direction on a straight line. They're both vectors. The first is orthogonal to the plane, while the second is parallel.

Here, according to the given information, we are given that,

The vectors are,

a = $i - 2j + 3k$ and this is projected on b = 2i + λk and the projection is 0.

Then, we have that, vectors a.b = 0.

Or, $(i - 2j + 3k).$$($2i + λk$)$ = 0

Or, 2 + 3λ = 0.

or, λ = $\frac{-2}{3}$.

Hence, λ = $\frac{-2}{3}$.

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