Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 8 Vector Algebra – I Ex 8.4 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 8 Vector Algebra – I Ex 8.4

Question 1.

Find the magnitude of \(\vec{a}\) × \(\vec{b}\) if \(\vec{a}\) = 2î + ĵ + 3k̂ and \(\vec{b}\) = 3î + 5ĵ – 2k̂

Answer:

The given vectors are \(\vec{a}\) = 2î + ĵ + 3k̂

\(\vec{b}\) = 3î + 5ĵ – 2k̂

Question 2.

Show that

Answer:

Question 3.

Find the vectors of magnitude 10√3 that are perpendicular to the plane which contains

î + 2ĵ + k̂ and î + 3ĵ + 4k̂

Answer:

Let the given vectors be \(\vec{a}\) = î + 2ĵ + k̂

\(\vec{b}\) = î + 3ĵ + 4k̂

Question 4.

Find the unit vectors perpendicular to each of the vectors \(\vec{a}\) + \(\vec{b}\) and \(\vec{a}\) – \(\vec{b}\), where \(\vec{a}\) = î + ĵ + k̂ and \(\vec{b}\) = î + 2ĵ + 3k̂

Answer:

Question 5.

Find the area of the parallelogram whose two adjacent sides are determined by the vectors î + 2ĵ + 3k̂ and 3î – 2ĵ + k̂

Answer:

Question 6.

Find the area of the triangle whose vertices are A(3, -1, 2), B(1, -1, -3), and C(4, -3, 1)

Answer:

The given vertices of the triangle ABC are

A(3, -1, 2), B(1, -1, -3) and C(4, -3, 1)

Question 7.

Answer:

Question 8.

For any vector \(\vec{a}\) prove that

Answer:

Question 9.

Answer:

Question 10.

Find the angle between the vector 2î + ĵ – k̂ and î + 2ĵ + k̂ using vector product.

Answer:

Let the given vector be \(\vec{a}\) = 2î + ĵ – k̂ and \(\vec{b}\) = 2î + ĵ – k̂