The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + z = 7 is:

$\sqrt{\frac{2}{3}}$

$\frac{2}{\sqrt{3}}$

2/3

1/3

Solution

$\sqrt{\frac{2}{3}}$

Normal to the plane x + y +z = 7 is

$\vec{n} = \hat{i} + \hat{j} + \hat{k} \vec{A B} = - \hat{i} - \hat{k} \Rightarrow |\vec{A B}| = A B = \sqrt{2} B C = L e n g t h o f p r o j e c t i o n o f \vec{A B} o n \vec{n} = | \vec{A B} . \vec{n |} = |(- \hat{i} - \hat{k}) . \frac{(\hat{i} + \hat{j} + \hat{k})}{\sqrt{3}}| = \frac{2}{\sqrt{3}} L e n g t h o f p r o j e c t i o n o f t h e l i n e s e g m e n t o n t h e p l a n e i s A C A C^{2} = A B^{2} - B C^{2} = 2 - \frac{4}{3} = \frac{2}{3} A C^{2} = \sqrt{\frac{2}{3}}$

Some More Questions From Vector Algebra Chapter

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Vector Algebra

The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + z = 7 is:

$\sqrt{\frac{2}{3}}$

$\frac{2}{\sqrt{3}}$

2/3

1/3

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The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + z = 7 is: 23 23 2/3 1/3

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Mock Test Series

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Entrance Exams Preparation

The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + z = 7 is:

$\sqrt{\frac{2}{3}}$

$\frac{2}{\sqrt{3}}$

2/3

1/3

Classify the following measures as scalars and vectors.
(i) 5 seconds
(ii) 1000 cm³(iii) 10 Newton
(iv) 30 km hr
(v) 10 g/cm³(vi) 20 m/s towards north

Classify the following measures as scalars and vectors.
10 kg

Classify the following measures as scalars and vectors.
2 meters north-west

Classify the following measures as scalars and vectors.
40°

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10^–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s²

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force