The projection of 2 hati-3 hatj+4 hatk on the line whose equation is overset arrow r=(3 + λ ) hati+(3 - 2 λ ) hatj+(5 + 6 λ ) hatk , where λ is a scalar parameter, is

Question

The projection of 2 hati-3 hatj+4 hatk on the line whose equation is overset arrow r=(3 + λ ) hati+(3 - 2 λ ) hatj+(5 + 6 λ ) hatk , where λ is a scalar parameter, is (A) (6/√41) (B) (32/√41) (C) (16/√41) (D) (7/5)

Tardigrade Admin · Accepted Answer

Given line is parallel to hati-2 hatj+6 hatk= overset arrow b (let) Let overset arrow a=2 hati-3 hatj+4 hatk Projection of overset arrow a on overset arrow b is ( overset arrow a ⋅ overset arrow b/| overset arrow b|) = (2 + 6 + 24/√41) = (32/√41)

Q. The projection of $2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ on the line whose equation is $r \to = (3 + λ) \hat{i} + (3 - 2 λ) \hat{j} + (5 + 6 λ) \hat{k}$ , where $λ$ is a scalar parameter, is

$\frac{6}{41}$

$\frac{32}{41}$

$\frac{16}{41}$

$\frac{7}{5}$

Given line is parallel to $\hat{i} - 2 \hat{j} + 6 \hat{k} = b \to$ (let)
Let $a \to = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$
Projection of $a \to$ on $b \to$ is $\frac{a \to \cdot b \to}{∣ ∣ b \to ∣ ∣} = \frac{2 + 6 + 24}{41} = \frac{32}{41}$

Q. The projection of 2i^−3j^​+4k^ on the line whose equation is r→=(3+λ)i^+(3−2λ)j^​+(5+6λ)k^ , where λ is a scalar parameter, is

41​6​

41​32​

41​16​

57​